When you let your subject know that they are working under a time limit, you undermine the trust and depth of the experience. This prevents the sharing of greater insights. If your schedule is truly tight, let the subject know at the start of the conversation. DO make eye contact. DON T be a slave to your notes.
Many interviewers avoid eye contact and focus on reading and writing notes during an interview.
Neither tactic helps you achieve a rapport. Without that rapport, your chance for a truly great interview is minimal. DON T end the interview without covering the bases. No interview is complete without checking to see that all of the bases are covered. DO follow up with the subject.