Paul,
Check for broken/loose/corroded wiring to the voltage regulator and alternator. You can take the alternator and have it checked, or try the voltage regulator first, as it's relatively cheap.
The small red indicator light is for the emergency brake and for the wear sensors on the front brake pads (if equipped and connected)
The GEN light should go out immediately after the engine starts, indicating that the charging system is working.
John
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