06 Element AT, Intermittent battery light

My friends element has an intermittent batt light, voltage at batt. and alternator checks out nominally, alternator was replaced with a new unit (I believe we used REMY) and upon discovering a crusty ground on the transmission we replaced the ground cable side of the batt harness. Battery is new and healthy.

This light has been mostly on for a year and a half. It started with the OEM alternator going out car had 300K+ at that time, So the alternator and batt. were replaced (new Remy alt), and a fresh batt. Light has not gone off since that repair. Looking into it we replaced the ground cable on the batt. seeing how much corrosion was on the transmission ground side. Light remains mostly on and sometimes off. No other electrical issues with the vehicle, vehicle runs and drives fine.

Thoughts?