I just went through something similar to this over the weekend in my 04' 5.4L. Never got a battery light on the dash though. First noticed low voltage when i went to use my wipers and they were moving slow...looked at the dash and saw my voltmeter was at just below half...put a meter on the battery and had 12.5 V while running (should be around 14.4V). Figured out that it wasn't charging. I took the battery and alternator into AZ and they both checked out good. I checked all 4 wires from the alternator and they all checked out, fuses also checked out. I went to put the alternator in and saw some rust on the alternator engine mount (where the lower two bolts are). I sanded down the lower brackets on the alternator itself where they contact the engine mount and also the steel engine mount points. Got it all together and it's back to normal. Looks like the alternator wasn't getting a good ground (from the engine block). FYI just checking ground from your negative BATT cable won't tell you all that's going on. Might be a good idea anytime you swap the alternator to clean up the engine mount surfaces as well.

 

Yes, that is the reason the alternator likes a ground wire to the frame.