Sounds like you might have a draw on the system. I recommend taking it to your local auto parts store and have the charging system tested. They should do it for free.
U may have a loose starter wire break in the cable etc. Also have you felt how warm the high and low beam switch gets in the steering column I had to add a head light relay kit to fix my issue LMC truck has the fix.
I took the negative battery cable off with the truck running, it dies immediately. The guy at AAP did a check on the alternator before I bought it, so it should be good. Where do the three wires go to coming off of the alternator?
just a little problem i found that will drain the vbattery when the charging system is all fgine that will prevent form charging right.......CHECK TO MAKE SURE THE STARTER IS NOT DRAGGING THE FLYWHEEL......IT WILL PREVENT FROM CHARGING THE SYSTEM RIGHT!
AS FAR AS THE TRUCK DYOING WITH THE NEGATIVE CABLE UNHOOKED FROM THE BATTERY, SOME ELECTRIC FUEL PUMPS WILL STOP IF THE BATTERY IS DISCONNECTED, I HAD AN EXPLORER THAT DID IT WAS A 1991 MODEL, AND I HAD A COUPLE OF CHEVY TRUCKS THAT DO ALSO, SO DO YOU HAVE AN ELECTRIC FUEL PUMP BECAUSE IT CAN CAUSE THE TRUCK TO DIE WHEN BATTERY UNHOOKED EVEN THOUGH THE ALTERNATOR IS CHARGING....