The stopping after a bit sounds like it could be the alternator, but I've found that usually it will squeal at a fast idle too, right after you start it up. But it's worse in the morning when there's a little more moisture in the air around here.
That could mean that it's still the alternator, but perhaps just that your belt is a little glazed over, and the pullies are dirty/slick.
Mine were. After a new belt didn't cure the squeal when I changed to a larger alternator, I found that a super cleaning of the grooves helped a lot. Used carb cleaner (Chemtool in my case) and a Scotch-Brite pad and some sand paper too, and got them "squeaky" clean (no pun intended) and that did the trick.
Unfortunately, it would only last for a few months at a time and then the squealing would slowly come back as things glazed over and deposits of rubber from slipping built up again.
My eventual cure was to go to a dual-groove pulley on the alternator.
Again though, this was due to me installing a more powerful and physically larger alternator on my Bronco. Same thing happens to at least half the people here that change out their alternators and keep the v-belts. Which is why I thought a picture would be a good thing so we can see if there have been any obvious changes from stock.
Good luck.
Paul