I had issues with the 2004 4.6 I had that the alternator would show a discharge while driving down the road. Then it would show a charge. I had it tested and the battery tested. All tested fine. Since I drive where there is no cell phone and lots of drug dealers in the brush (yes, the Texas/Mexico border) and couldn't afford to be in a questionable vehicle, I had the alternator swapped out for a new one. Cured the problem. The issue was the alternator would charge and test out fine. But then when it got hot, it would stop charging. Since you don't have a meter, the gizmo glc recommended would certainly tell you what the voltage is in the system when the light comes on. If the light comes on and the voltage drops, you likely have the same problem that I did.

 

Update - took to a shop and they found the alternator was bad. It was intermittent failing so i guess AutoZone and o Reillys couldn't catch the fail on their machines.

i got a motor craft reman from car quest and installed myself. So far so good. Thanks for your time and help everyone.

edit disregard that damn it light just came on and went off

Ok this is odd. I read on any older ford thread to check #11 and #17 fuses in fuse box. The 17 looked like it was in slightly crooked. I pulled both out and checked to make sure they were not blown and put back in. Today no battery light on all morning.
Could that have had something to do with it? Battery light comes on at first when all instrument panel lights up then goes away like normal. So far so good.