I don't know how Gil treats Parker, but Gil seems to have started touching Parker very early, but Gil is not the kind of person that all men he will touch. When Walter was surprised that Gil had never touched Parker, Parker's answer was very unnatural. He summarized the reason as Gil's strong hormone secretion, which seemed like a lie. But from Gil episode, we can know that Gil used to be a pure person, which is a little contradictory.
When Gil touched Walter in high school, maybe Parker had left. But when Parker came to haywell, Gil began to treat Parker as before. Although Gil asked Parker to stop Gil's sexual behavior, Gil would still touch Parker and make some sexy jokes with Parker.