Been seeing this for a while now, namely that the battery light lights up intermittently when the engine is cold. So it's not on constantly. Once the engine reaches higher (operational) temperatures however the light switches off and remains off.

Already had them check the battery and the alternator, which both read good voltages even with full drain on the electrical systems. Verified the codes via an OBD2 reader when the light was lit, and no codes were present.

Also the charge indicator...

Battery light illuminating when engine is cold - 2002GT