My T is very closed and blank slate too. He still seems genuinely warm and kind towards me though, so I haven't let it get to me that I don't know much about him. I don't even know if he's married, and I've been seeing him going on two years.

He's very much about CBT, and from what I understand, cognitive therapy T's tend to be less about touchy feely emotion and more about thinky thoughts.
Once we were talking about my trust issues and he asked if I trust him and considered him kind. I gave a tentative yes, but that I don't actually KNOW him, so I couldn't say for sure. To which he replied, "No, you don't know me outside my role here, and that's how it has to be. I can't be your friend."

So I"m always reluctant to ask him anything personal at all.
Every so often I'll get tidbits of information on his life outside the T role, and I memorize it. I do wonder how different I would feel towards him if I knew more about him.
I think T's should at least be warm and kind feeling, even if they are a blank slate otherwise.