Hmm - hooked up a jumper cable to the IGN terminal on the regulator. I had the IGN wires unplugged from the tab, just pulled it off and hooked up the jumper cable. I connected the other end of the jumper cable to my battery (to the post connector, not the post itself). Still had the voltage draw. I did this once with a set of jumper cables, and a second time with a set of test wires.

This would seem to me that it IS the regulator itself. Can't buy one at the local parts store, have to order it.

I know, I know, I was told to do this first. But it sure seemed unlikely that this would actually be the real problem. I won't know until I pop in a new one.