[steelybill]

You may have a wire being grounded somewhere between your GEN light and the alternator. The light has battery voltage on one side, and the alternator supplies the ground when the ignition switch is on with the engine not running. When the engine is running, the alternator has battery voltage on the the light instead of grounding it, which means no current flow through the light, and it turns off. That is controlled by the voltage regulator diodes in the alternator.
It could be other things also, like maybe the ignition switch etc
There is also a diode in the light circuit to keep the alternator from supplying voltage to the ignition when the ignition switch is off.