All appears to be okay re charging system and battery.
The battery went dead overnight a couple of days after the low fuel sensor came on and stayed on...with a full tank.
I charged the battery and checked for parasitic draw with the key off, and there was none.
I unplugged one tank connection and the fuel pump made unhappy sounds. I re-plugged it and unplugged the other.
The fuel light stays off. The fuel pump sounds happy. Battery reading at off, key on, idling, and cruising revs all look good.
So I'm going with the shorted fuel light theory. I may ride it to work tomorrow...