My first T said several times that apparently many therapists go over time because they don't feel they are doing/helping enough and want to do more. Don't know if that is true. My second T went over the 45-50 mins often, not very much but 5-10 mins and it wasn't consistent. He definitely looked like he was doing it because he enjoyed the interaction and that was also my reason to stay for it.

I saw when they had positive feelings/motivations just like in any other interpersonal interaction, from subtle non-verbal signs to how they engaged with me. It never even occurred to me to doubt it. Similar for when they seemed less interested, engaged, distracted and obviously not fully there in mind. I am not sure these things always indicate their feelings toward the client though, I think it is often just a default mood state they are in.