That's interesting.... I've had my fuel gauge suddenly drop to empty a few times in the last few weeks, and when it does the fuel light comes on. When the gauge starts working again and goes back up, the light goes off.
I would pull the dash out to check the connectors on the back. If everything looked good I would try applying a 9V battery (should be enough current to move the dial but not enough to hurt anything) across the gas gauge bolts that connect the wiring to the dash to see if the gauge moves at all. If it moves, it would seem like a broken connection somewhere. If not, I would replace the gauge.