Battery Light on

Thanks for the replys, so I did a test and swapped out my wifes battery and put it in my truck and let it run for a few minutes and the gauge didn't go off.. I ran a few more tests today with my multi meter and recorded the numbers:

Battery with engine off cold: 12.7V
Truck running with lights and ac on was 13.7..


13.7 is on the lower end?

 

See below link.
https://shop.advanceautoparts.com/r/advice/car-maintenance/symptoms-of-a-bad-alternator
Seriously before I just shotgunned it and put in a new alternator when that would be a hope and a prayer (voltage looks ok and you had it checked ok) I would ask the dealer how much for an electrical diagnostics test. If you want a free wild hair test or two before doing that:
*Check connectors at alternator are tight
Edited: fuses I had listed were for 2016-2019, the below is for 2nd gen:

* Check fuse 7.5A ALT-S. See the diagram below for the sensing circuit path, with the red arrow, check fuse and all connectors in this circuit:
http://www.bodenzord.com/archives/477

I did find where someones alternator checked "good", but replacing it fixed the problem. On the other hand, this guy found a broken wire was the problem, AFTER he had replaced his alternator AND his battery:
https://www.toyotanation.com/threads/charging-issue.468241/
My wild hair guesses are free and the value may be worth that

 

Just wanted to put an update out on this. I changed the alternator yesterday(Denso) and belt while i was at it, let it run for about 10 minutes, drove it around the block and the check engine light still is on. I tested the battery again with multi-meter just for sanity and its fine.

Only other thing I can think of before I bring this to the dealership is, possible fuse issue or wonder if the wiring that is wrapped up with that goes from the battery to the fuse box, or the alternator wiring is damaged.. I am assuming there is small wires inside some of those harness's..

 

sorry, missed Davids response and just saw it after mine.. I think this is the route I am going to take.