T1 does a lot. In some ways it has been helpful, because it has strengthened the relationship. I'm sure part of the reason I can be so open with him is because he is so human.
Sometimes though he gets self disclosure wrong and it can be a bit too much information. For example, I was once talking about dissociation and he asked me a question about it, then related it to himself, going into lots of detail about a dissociative episode he once had. this wasn't useful and felt like it was turning into his therapy. I think he was trying to let me know he could relate, but things like that increased my transference towards him that relates to having a mentally ill mother who couldn't be there for me emotionally.
T2 has told me nothing about his life, but I think he is especially careful because he knows how hard transference with T1 has been.