Does dissociation result in not being mindful, or does not being mindful result in dissociation?

I would answer this (for me) that they are two different things. For me dissociation happens, I don't chose it - I have a hard time getting out of it. Mindfulness is something that can be worked on by paying attention to the current moment. So in short, (again, for me) dissociation results in not being mindful. Two separate things that by using mindfulness I can try to overcome dissociation. That probably doesn't make any sense. This is something worded a bit better (Mindfulness vs. Dissociation). I agree more with the Mindlessness is an issue and Dissociation is an issue each have their own different underlying reasons for occurring but you can use mindfulness to help overcome dissociation. That was a rambling circle of words - hope it made some sense.

Is not being present in a session always mean you're dissociating? I'm confused because lately I'm not present, or not mindful, but I don't know why that happens. Like when I hugged my T last session but didn't feel it. I know I was hugging her but I didn't feel it.

No. Sometimes not being present is just the mind saying 'nope, not today can't handle anymore' but that doesn't necessarily mean dissociation. I also suffer from both derealization (foreign world) and depersonalization (not with my body). So a lot of the time I can't feel my body because my mind separates it from me.

I was away last week so I didn't have a session. I want very much to be present tomorrow. I want to be able to look at T and not look through her.

Can you work on this with her? Tell her that you want to work on seeing her and not looking through her? Could your non-presentness (I know not a word) be a result of fear of connection again? Or the strength of that connection? Hence, not feeling the hug from her - you want it but you don't? When I'm feeling like that in session we spend the session working on looking at her, telling her what I'm seeing, talking to myself to her about everything going on through my eyes and my body and I find it greatly helpful and something I'm finally learning to use in my everyday life, on my own without her prompts - they are becoming 'natural' to me to focus on every little thing during the day, telling myself what I'm doing, how it feels etc.
Not sure if any of that helped feel free to PM me if you have any questions, etc. That's my "two cents" on the topic.