One side of the lamp goes to the alternator (via the wiring harness and relay box).
Other side goes to the battery (via the underdash harness and associated sources wires, same circuit as other indicator lights).
Light comes on when there ~5 or more volts between the two. When the key is off there should be zero differential (0V - ground - on both sides); with the key on, battery voltage differential (~12V on one side, ground on the other). With the car running, zero differential (alternator output of ~13.5V on both sides).
First, pull the gauge and see if the right wires are connected. One should be blue, the other red/white.
Second, check your fuses. Your lioght is powered by S9.
Third, are all other gauges working correctly? Are there any other electrical anomalies?
Finally, with the car off, use a VOM or a test light find out which side of the light has power; is it the blue alternator wire or the red/white dash wire? Neither should have power with the key off.
Troubleshooting electrical issues over the Internet is soooo fun....
Greg