I have searched the site and found many similar problems however nothing exactly like my situation. 1999 F-150 4x4 with 5.4. Driving home voltage gauge in dash shows volts dropping rapidly. Finally battery light comes on. If I revved the engine voltage gauge comes up and light goes out. When I get home battery is dead, won't start truck. I think Alternator or battery. Have alternator tested at two different places and it checks good both times. In fact second place tests 3 times. So, I replace battery as my home charger can't seem to top it up and charge window shows red on battery. Not convinced that alternator is charging new battery. 12.4 V on terminals, 12.6 when engine running. If I measure current, most is flowing out of the battery at idle and some flows in when I rev the engine. I'm not sure if that is enough to charge the battery. Does the battery not charge in idle? So, checking wiring. Haynes manual shows two Mega fuses on firewall behind battery. Not in my truck. Where are they? In my truck the main cable from the alternator goes to starter relay then not sure how it gets to the battery for the charge. Alternator field fuse is good. On the battery there are two heavy red cables molded together at the + terminal. Where do they go to? One of them has a fusible link. Not sure where it goes. Any suggestions would be welcome as Haynes manual not overly helpful.

 

At idle the charging voltage should be 1.5 to 2 volts higher then the battery voltage, this is with no lights or other accessories on. 12.6 is way too low, so unless you have some heavy corrosion on the grounds, or charging circuit wires,I would suspect the alternator. It should be putting out at least 13.5-15v at idle.
The two red cables from the battery positive terminal: One should go to the main fuse box, and the other to the starter or starter relay. In your case you said that the thick wire from the alternator goes to the starter relay, so one of those red cables from the battery should be landed right next to the cable coming from the alternator, so you should have two wires right on top of each other on the same bolt.

 

Yep it sounds like your alt is failing. It wouldn't hurt to check the reference voltage on the field wire.

 

Replaced the alternator and problem fixed. I guess the two independent tests showing the alternator good distracted me from logic.

 

Glad to hear you got your problem fixed.