Ahhh, just for the record...
It was... the starter switch, which was working normally as far as starting the engine goes but not working normally as far as reconnecting the headlight / tail light. I didn't figure it out until I took apart the whole starter / stop switch and found that the switch itself had been 'repaired,' at some point, by which I mean duct taped together. The plastic was totally friable and fell apart in my hands. The contraption has worked flawlessly for the 6 or 7 years I've had the bike, amazingly.
Out of curiosity... how do you put those back together when the plastic *isn't* falling apart? The little roller-ball looks like it has to be precariously balanced while the rocker plate is suspended and floating upside down in the little brackets. Telekinesis? WTF?