Battery light...for no reason?

Never had this before and only posted in general to reach a broader audiance. Drove to work today and every acceleration the volts dropped from 14ish to 13ish. Got EVERYTHING tested and battery came up bad. Replaced it and drove home, gauge only moved a smidge once from 14 to 13.99. Parked the truck and went inside for 2 hours. Came out to leave for mcondals truck sits at 12 volts and battery light. But the truck runs COMPLETLEY FINE, have 1000 watts of audio and all my accesserioy lights on and put as much load as possible and the truck had 0 issues. But the light is still on and the gauge says 12. Im super lost any ideas?

 

either battery or alternator..... my battery light turned on when my battery died, but my volt meter was dancing when I hit the brakes, so I had to hit the gas like if it was 1970 so the truck wouldn't die... when I accelerated volt meter came back to normal.

 

I would say yeah if the alternator didnt pass an bench test and the battery was just put in today

 

Seems like you may have a loose connection on your main ground.