I don't think Gil and Parker have that kind of relationship. Parker once said that his relationship with Gil was not as close as Lars × Gil.Lars and Gil, mark and Anders, explicitly mentioned that they had been in love. Only Parker didn't. He seemed to be the one alone.I think it might be Parker × Walter.
I wonder if Parker has ever been in love? Who is the person he once loved? Walter？ Or does Parker have no love experience?