This happened to my 2004 Ford a few years back and it definitely was the alternator... I replaced it with a NAPA rebuild and got it all installed and working in just a couple of hours...
The Alternator goes through almost the same DC VOLTAGES OUTPUT as the RV Converter/chargers do... (14.4-13.6-13.2 etc) I don't remember the exact DC VOLTAGE levels but did see the three different levels of charge...
After I replaced the alternator and reconnected the batter cables etc everything on the Truck worked just fine except the IDLE SPEED. It was very low around 400RPM or a tad more. I have read that this is normal and should fix itself after your drive it awhile. I went for a whole week keeping my foot on the gas pedal keeping the truck engine from stalling out at stop signs...
Since there are NO MANUAL SETTING for idle control like in the old days I finally gave up and took it into FORD to reset the computer settings... Cost $90 for about a five minute reset effort... geesch...
Worked well until I traded it a year later for the 2010 Ford Truck I have now...
Since then I have been extra cautious of pulling my main battery connections from the truck electronics. I used to do that alot resetting fault readings from various things... Not any more haha... I wire in a second battery to keep the Electronics live now when I am working on my DC CABLEs for my Ham radio setups...
Me too broke to have to pay those $90 computer resets...
Roy Ken
My Posts are IMHO based on my experiences - Words in CAPS does not mean I am shouting
Roy - Carolyn
RETIRED DOAF/DON/DOD/CONTR RADIO TECH (42yrs)
K9PHT (Since 1957) 146.52M
2010 F150, 5.4,3:73 Gears,SCab
2008 Starcraft 14RT EU2000i GEN
2005 Flagstaff 8528RESS