Battery light

2001 V6 was washed today (Michigan Weather) and a few hours later the battery light came on. I revved it a little and the light went off. So I ran to the store and came back to check the voltage. It was in the 13's until I shut it off and restarted. now reading 12's with the battery light on. I revved it again but no change. It's all original, belt, alternator. Anyone change one on a V6? Hard?

I have noticed that if I have taken off from a light hard (high revs), the battery light would flicker, but never thought about it

I changed one on an 03 ford escape 4x4 3.0 v6. it took me like 3 hours. it's no fun but it can be done.