I lucked into the website of a man who bought a bunch of these machines at auction and learned how to repair and maintain them. http://www.truetex.com/icemachine.htm
In reading through his articles, I was able to pinpoint the problem- the pump that circulates the water from the reservoir over the freezing tray. I found the part at appliancepartspros.com. My order came in just a couple days. The actual repair involved unplugging the machine, removing some hex screws, the reservoir and the cover to the pump. Then it was just a matter of detaching the pump and mounting bracket. The new pump plugged in and then I was able to reinstall the other parts. Thirty minutes later I had my first ice drop. The most difficult part after diagnosing the problem, was removing the hex screw from the back corner of the pump mounting bracket, probably due to a too-short screwdriver in a very confined space.