I consider that rude behavior. Why not call him on it? You could simply ask, in a very open way, "why do you avoid my gaze, stare at the wall, and say nothing when I say ______?" Maybe you will learn something that will help you interact with this T. Maybe he will learn something about how rude he's being.

There is the blank slate kind of T who doesn't like to reveal anything about their personal life, but usually this type will respond to a client query with, "what does it mean to you that I may be ________?" Or "how would you feel if I was ______?" Or some such question-in-return comment. But your T is not reacting like that...