I don't really have a straightforward answer. The first T I saw I took a long time opening up because I was very guarded and closed off. I wasn't used to being totally open with people, it wasn't really their fault. It was probably a year or more. My second T also took a while, though not as long. At the start I was able to open up in kind of a this is what happened sort of way but not in a this is what I am feeling kind of way. Eventually I was able to let myself be totally vulnerable because I trusted them and they had shown that they were trustworthy. Other T's have been similar but most have just been surface deep. I'm more open at the start with what I am dealing with or what I have dealt with. The trouble I have is connecting with a therapist and feeling comfortable being vulnerable with them. So not just saying X happened but saying X happened and it made me feel Y and it hurts a lot. It takes a while for me to trust and feel able to express emotion.

I agree that the initial gut feeling of connection can make a difference. Sometimes even though there is nothing wrong with a therapist, they just aren't the right therapist for you at the time.