Ok, here's the news:
OFF: the battery was about 11.8 volts.
On: with headlight on about 9 and change volts.
Starter depressed: 7.4 volts and dropping
When I pressed the starter, the bike made a very slow, gutteral, clicking/chugging sound and the volts dropped to 7.4. When I held down the starter for a couple of seconds the volts slowly dropped till I let go at 6.8 volts. When I tried to repeat the test, nothing happened when I pressed the starter. No sound, no drop in voltage, nothing. This is how it usually goes until I jump the battery again.
Help . . .