I think you are right gerber, about paying attention but I also think there is a healthy dose of caring too. There are plenty of times, at least 4 that I recall quickly, I have cried talking to someone in crisis (i was on the phone and they didn't know I was crying.) If I didn't care, I wouldn't feel that way. I remember crying over the suicide calls and the distress they felt. Trying to at the same time, use the protocol for suicide calls and not sound like I feel badly for them if you know what I mean.
I think you might want to make an impact in some way on your T's life. And yes, you do that. Absolutely. Each life that touches ours makes an impact and is unforgettable in it's own way. It's true, I may not recall everything about everybody all of the time, but I remember the impact people made on me and hopefully I made some impact too.
Keep writing! And yes, your T does care! For sure!