Call the medical student clerkship coordinator and/or director (I always started with the coordinator and worked up) and talk to them about your sincere interest in their program.
I got one of my aways off the wait list. They sent me an email saying that all their spots for the date I requested were gone. I emailed the clerkship coordinator asking them to keep me in mind if a spot opened up. The coordinator emailed me the same day to offer me a spot that just opened up.