Shame is a very painful emotion. I have wondered about the eye contact thing too because I have noticed that the harder it is for me to express an emotion the more likely I will find that I read it (then I don't have to see T's reaction.) I have also seen shows on TV where the person doesn't want to see the person when he/she tells them some really tough stuff. I usually look at T unless I am expressing an emotion (annoyance with T) that is just plain extremely hard for me.
Firstly, different cultural groups will look into people's eyes less than others. Sometimes, refraining from making eye contact is a sign of respect while making eye contact may be seen as a challenge.
I feel more vulnerable when I talk to T. I suspect that looking into the eyes of T might make you feel more vulnerable. (I make eye contact on a more conscious level rather than sub-conscious because I don't like to make eye contact with other people.) I got teased in school and repeatedly accused of starring at people (starring at wall until person enters line vision and I continue to stare). Then he/she thinks that I am starring at them when I am hardly even percieving the outside world.
Eye contact might also deepen the connection between you and T. Maybe it helps you to distance yourself a little.
As for trusting T, that takes time. I tend to relate to certain people (men in authority over me) like they are my step-father. It takes time and a lot of effort to change ones automatic way of responding to others. It probably took you years to learn to dissocate in order to survive in your family and it will take a while to learn other ways to relate to people. I hope you hang in there and keep working at it. I am glad to hear that you can hear concern and empathy in T's voice. That sounds like progress to me. I remember the first time that I thought T cared about me. My mind played that line "____ cares about me." over and over again.