I am/was not aware that it is possible to force a zip drive to spin continuously. I recall having tried very hard to do this for some benchmarking that I wanted to try out. No joy. Given that the head is in physical contact with the media, I was not surprised that the engineers at Iomega had made that choice. But now it seems that I may have drawn incorrect conclusions, and there may be a firmware rev (for example) that does allow such a thing.

Are you sure that it is spinning autonomously? That is, are you truly not seeing the drive light blink during this time? The "normal" way a zip disk operates is that it continues to spin for some number of seconds after the most recent access. Then it spins down. If accesses come at a high enough rate, the zip will keep spinning. Is it possible that you are running some sort of background app (or have a virus) that keeps pinging the disk?