Are Yale campus interviews generally timed (as in the interviewer has to finish in 30-45 minutes)? How are they in general?
It might depend on the interviewer. I’ve heard 30 - 60 min. and I know someone who is an alumni interviewer for another Ivy and tries to stick to that rule for the most part, though he told me it might go longer if there is something particularly engaging about the applicant. I wouldn’t read much into an interview that’s under an hour, and those that run long are probably far more likely to get the applicant’s hopes up than result in an actual admission.
How long I spend on an interview is a direct function of what else I need to get done that day.
I can usually tell within the first 15 minutes whether a candidate is competitive, and I generally have enough material for a detailed interview report by the half hour mark. I wouldn’t worry if an interview is short.
Also, just because you have a good rapport with an interview doesn’t mean that you’ll get a good interview report. The reverse also holds true. I have recommended students previously to not be admitted to Yale (due to poor fit, insufficient intellectual depth etc.) even though I enjoyed our conversation.
All Yale campus interviews are done by seniors, not alumni. Depending on how it is going, it could last 30 minutes to an hour. Alumni interviews probably run about the same. If the student gives me a lot of one sentence answers, I may wrap up in half an hour. Otherwise, we may go on for up to an hour.