I think this definition is unclear in ways that have allowed you to interpret it differently than I would, and that kind of ambiguity bugs me when it comes to a term people are going to take legal (or other punitive) action based on.
You and I agree that:
a) It is not a victim's fault if they are sexually harassed
b) It is possible to sexually harass someone without touching them
Here's where you and I diverge somewhat. You say that "it is not up to the perpetrator to determine if his conduct is within the appropriate social norms, traditions, or customs for the time and place. It is solely how the victim perceives his behavior as being unwanted and sexual in nature." Let's break that down.
Point 1: A perpetrator does not get to determine whether what he did is within appropriate norms of time/culture/place.
This is accurate in the sense that you can't just decide that something is okay and that means it is okay. Furthermore, I think that while some behavioral standards are influenced by time and place, consent is consent (and nonconsent is nonconsent) and basic fundamentals of morality are constant through time and culture.
Point 2a: Sexual assault is determined solely by the victim feeling that s/he does not welcome the behavior...
Point 2b: ... and by him/her perceiving the behavior as sexual.
These are where my biggest problems with your interpretation lie, I think. In general, I think that crimes should require intent (or, as it's referred to in law, a mens rea or evil mind) as well as doing something that causes a bad result (the actus reus" or evil hand). Though some crimes are statutory and have no mens rea, it's probably not a great idea to eliminate the requirement generally for reasons I don't want to dive off into here. (Submit another question if interested).
This does not mean that someone must intend to sexually harass you, because there are various states of mind that will suffice for a mens rea, depending on how we choose to write and adjudicate our laws. For something like sexual harassment, I'd probably favor a definition that included lower mental states like "recklessness" or "wilfullness." (e.g. it's harassment if a reasonable person really should know that you don't welcome this person's attention, but they're super stupid about it, or purposefully trying to ignore your "no" signals.)
What I take issue with is the fact that you've eliminated any objectivity by determining that both welcome/unwelcomeness and sexuality of conduct are determined internally by the victim rather than based on some sort of objective standard.
Most people who sexually harass someone will know that their actions are unwelcome. However, it's problematic to convict people of crimes (either legally or in the court of public opinion) based on criteria which could be invisible to anyone but the victim.
To be clear:
-Someone about to act sexually towards another person is responsible for ascertaining consent
-Every individual always has the right to refuse or withdraw consent
That's not really what we're concerned with here, though. My concern with your interpretation of this definition is summed up by the following scenarios. I do not suggest that these situations represent the majority of sexual harassment, but they could (and may actually) happen and that means that the definition needs to account for them.
Hypothetical 1: Carol is a friendly worker who greets each co-worker as they pass her receptionist's desk. She likes to compliment people and will often congratulate them on work-based accomplishments or mention things like new haircuts or glasses or such. One day Carol says to Dean "I like your plaid shirt Dean, lookin' good! Have a great weekend!" as he leaves the office. Dean thinks that Carol's comment on his shirt is sexualizing him, because he is a bodybuilder who works hard to build up his pectoral muscles, and because he thinks she knows he has a photoshoot as a swimsuit model this weekend.
Problems: Carol may not have even known that Dean had a swimsuit shoot this weekend, much less been making a creepy allusion to how Dean's pecs would look during it. All she meant to do was to compliment his tie, and 99 people out of 100 would perceive no problem here. However, if Dean gets to determine what behavior is sexual (rather than a reasonable, objective standard being applied), this constitutes sexual harassment if Dean didn't like it and thinks Carol meant it sexually.
Hypothetical 2: Geoffrey is on his second date with Linda, a girl he has been friends with for a few weeks. They are watching the newest season of "Great British Bake Show" in Geoffrey's apartment, alone, after eating dinner together. Geoffrey says to Linda "Can I hold your hand?" Linda says yes, but is secretly uncomfortable because she has already decided that she doesn't want to go on another date with Geoffrey. Linda isn't happy about holding his hand, but doesn't want to say no and make the rest of the night awkward.
Problems: In most real-world situations, there are ways to tell that someone isn't into you or they'll tell you. However, there are also scenarios where people intentionally hide what they're feeling.. In these situations, I don't think we can hold someone else responsible for knowing that another's feelings on welcomeness differed from what their actions portrayed.
I'll restate that these scenarios are not what we are usually concerned about when we discuss sexual assault: we are most frequently concerned about situations where it's pretty clear that something was both sexual and unwelcome to all parties: victim, perpetrator, and objective observer. While ambiguous cases like the above may occur, what people commonly mean by sexual harassment is much more clear, harmful, and blatant.
But when we set up a rule that's going to define when people get punished for something, I prefer it to be inclusive of not just the most likely scenario, but of less-likely-but-possible ones as well. Accordingly, I have problems with the way you've read this definition, and thus with the ambiguity in the definition itself. I think a definition for sexual assault must clarify the standards by which actions are evaluated, and I don't think that relying on things that can occur solely in a victim's head (even if they usually don't) is appropriate when it comes to punishing someone else. If we only look at the victim's mind, we run the risk of punishing people for behavior that they didn't and shouldn't have had reason to know was wrong.
So what would I change? I'm reluctant to come up with my own word-for-word definition because it would probably be inadequate in many ways. That being said, here are elements I think we need to get across in defining sexual assault for legal purposes, and that we should consider when deciding whether an accused perpetrator deserves non-legal punishments (like shunning, job loss, etc).
1. A perpetrator who does something that they know or that, interpreted by a reasonable person with knowledge of relevant context, is sexual.
So, I want something that's objectively sexual to have occurred. This will vary by context.
A man walking into an LDS Relief Society meeting wearing a Speedo and interrupting the lesson to stand with his groin at eye level in front of the woman who refused to date him may well be sexual (and unwelcome, but we'll discuss unwelcomeness next). However, standing around in a Speedo at the beach while you enjoy the waves at your feet is probably not.
Pulling off your friend's wig as part of a prank war at a Halloween party is probably not sexual, but pulling off the wig of a Hasidic Jewish coworker may well be.
However, we can look objectively at those situations, if we know the relevant context (things like: history between the people concerned, the location, the culture and individual history of the people concerned, etc.) This enables evaluation according to an objective, reasonable standard as to whether conduct should be interpreted as sexual. It lets us know whether someone should have known what they were doing would be seen as sexual.
2. A perpetrator who does something that they know or that, interpreted by a reasonable person with knowledge of relevant context, is unwelcome.
So I also want something that's objectively unwelcome to have happened. Again, the context matters.
A woman who says "I really need to go to work" when her husband goes in for a kiss in the morning, but who continues to kiss her husband may well be happily consenting despite her protests about the time. If we know enough about the couple's relationship dynamics and current circumstances, we may be able to interpret the ensuing makeout as fully consensual even though the same words could indicate a nonconsensual encounter under different circumstances. (For example: the same woman saying that she needs to get to work to the creepy guy who's following her on the sidewalk trying to invite her to coffee at his apartment.)
Again, this objectivity allows us to evaluate whether the perpetrator should have known that his actions were unwelcome (and thus harassment).
Note: In my opinion, it is possible to be hurt by the actions of another and for your pain to be real, even if what they did does not qualify as "harassment" under these criteria. We should support those who need our help dealing with pain and sadness. However, it is also important that we do not set up definitions that assume that any time one person is hurt another person must be legally (or morally) worthy of punishment.
Essentially, here are the possible scenarios
1. The perpetrator and an objective observer can tell that the victim would be offended by the sexual act: This is harassment.
2. The perpetrator does not know the victim would be offended, but the objective observer can tell. This is probably still harassment, because it's important for society to have reasonable standards of actions. You can't go around harassing people or committing crimes just because you're stupid or purposefully ignorant of basic behavioral standards.
3. The perpetrator knows the victim would be offended, but the objective observer doesn't know. This is the concerning situation. I acknowledge the troubling possibility that there is secret knowledge held by predators that doesn't make it to a jury or any other observer that enables the harasser to use externally reasonable behavior to harass someone. Such action is clearly immoral, but I do not have a good answer to how a morally sound and consistent legal system can identify and punish it without using rules that are subjective and/or creating a risk of false conviction (the prevention of which is a major fundamental of the American legal system).
4. The perpetrator does not know and an objective observer does not know that the action is sexual/unwelcome. In this case, we should still seek to help the person who is feeling pain or sorrow, but I do not think it's moral to punish someone for something they couldn't have reasonably known was going to hurt the other person.
In summary: The two elements I suggested above (objective sexualty and objective welcomeness) describe how we can evaluate someone else's behavior without having access to their brain, and I believe that this is the standard we should generally use for law and one we should frequently consult (though not necessarily always emulate) for social or other institutional rules/standards.* It doesn't seem fair to me to use the internal workings of a victim's mind as the sole determinant of what is and isn't sexual harassment. In order for sexual assault to mean something other than "Something I don't like," I think there needs to be a tether to an objective standard. However, objective standards like these never excuse immorality: Each of us is accountable to ourselves and to God for our own motivations and actions, and we won't get off by saying that something we knew was wrong even if an observer couldn't know that.
This is a long-ish answer, and I hope I have written it well enough to make it clear that: 1) Sexual harassment is never acceptable and is always immoral and sinful and 2) it is important to have objectively discernable criteria for determining what qualifies as harassment when we will label and punish someone as a harasser.
*It's important to me that the legal system err on the side of avoiding false conviction. By contrast, there may be times where social or other institutional sanctions, punishments, or even just adjustments are appropriate with less evidence. To make an analogy: criminal cases usually require conviction "beyond a reasonable doubt" while civil cases may punish someone if the evidence is "a preponderance" (basically >50% chance). If we're only 51% sure Jerry harassed his coworker Kelsey, I don't want Jerry in jail, but I'm fine with his company choosing to fire him or relocate his position to another office.