Battery light on, truck battery & alternator are good

Hello.
2007 2wd Tundra w/V6. Bought it from a friend last year to use as a work truck for a new home build. Moved into our new home a few months ago, and so I'm ready to sell it but the battery light is on.
FWIW - the light came on shortly after I purchased it. Distracted by home building, didn't have spare time to isolate to the root cause. I did keep a VOM in the truck to check for alternator output from time to time. Alternator output was - and still is - acceptable.

Before creating this post, I checked and the battery has 12.85 volts at rest, then jumps to 14.2 volts when the truck is started.

I'm looking at the wiring diagram, specifically, the four wire connector at the alternator. Trying to figure out which wire is associated with the battery light on the dash.

Red wire goes to the engine control module.
Green & yellow wire goes to a 7.5 amp fuse called LH-IG (ignition ?)
Black & yellow wire goes to a 5 amp fuse called ALT-S
Black wire runs in parallel to the main power output wire going back to the battery

was thinking this is a ground issue, but no ideas where the ground for the battery light circuit is.

is there any experience on this forum with a nuisance battery light ?

 

Someone else was having a similar issue. It was with the 5.7 I believe, but electronics will be similar across the board with minor changes here and there. You can also look at the wiring diagram posted on this site.

 

You may still need an alternator. Sometimes a diode will fail in the rectifier. DC voltage will still show good.