Hi Dotti,
Thank you for the kind words about the listening approach in developing rapport with students. It is essential as you well know.
Your question is a tough one to answer as so much of the answer depends upon what the student will volunteer as you mentioned. My approach has been to have a one on one private visit with the student and talk about the class and that student's position in the class. Generally if something big is going on in their life they will be having problems in the class, with late assignments or poor test performance, etc. Talking about the problems and me asking them if there is anything I need to know about how to help them opens the door to them telling me what is going on. This way I have not invaded the privacy of the student but have expressed my concern for their success.
Gary