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I would tend to not trust idiot lights over a gauge that is correctly hooked up.
Not familiar with your set-up but on my 2000 diesel, the automatic belt tensioner will take a 1/2" breaker bar to loosen the belt, just tie it down to loosen the alt. Label the connections.
Charlie's advice is spot on especially about the connections etc. There is a fusible link running off the alternator that seems to be potentially problematic--might be smart to check the entire charging circuit properly before assuming its the alternator itself.
The only time (so far) I've changed one is on my '00 E250 with 5.4 gasser--took all of 1.25 hours start to finish on the coldest day of the year at that time. This included removal, picking up and installing the new one. Also good to checkk the serpentine belt and tensioner while you're in there---doesn't hurt to inspect and/or replace either at this time.
Actually if the fusible link is burned or open that's a bit easier to change and less expensive than the alternator. Where exactly did you test for output---at the alternator terminal itself of elsewhere?
At the battery terminal located on the alternator is the best place---anywhere else and I'm guessing you'd be after the fusible link. If that is open no charging indication would be seen.
Piece of cake to replace. It wouldn't surprise me that the alternator took a dump. I took one from a 5.4 in to be rebuilt at around 115k from an Expedition and the guy at the auto electric shop said that they see it quite a bit because of the slip rings. It was $120 or so to have it rebuild and the output boosted.
Check the tensioner as well. I just replaced the tensioner on our 06 3/4 ton van with a 5.4 at work with ~115k on it because the pulley bearing was toast.