How do we prevent people from going into a locker room (where there is no doubt what plumbing they have) just to get their jollies while claiming they belong there?

Repeating what I mentioned in my prior post - by looking at whether the person actually has done anything to support their claim that they're trans. Have they asked their close confidants to call them by a different name or pronouns? Have they spent some period of time adopting the outward appearance of their identified gender? Have they spoken to a therapist or counselor about their gender dysmorphia? Etc. Someone who has never ever done a single thing consistent with transitioning isn't going to be able to convince a court that they're actually trans - so all you need to keep them out of the locker room is to maintain the same sanctions that apply when you go into the locker room of the opposite sex to get your jollies. Whatever works to keep men out of the women's locker room today is still going to work in a world where trans people have rights.