My money is on a bad battery. Start the truck and increase the RPMs. Take a screwdriver and stick it up to the rear bearing on the alternator. If it sticks to the rear of the alternator then its charging. You could have a diode out in the rectifier bridge causing some bleed back on the battery but the only true way to tell is with a hi tech alterator testor or test the individual diodes with the alternator apart. I would have the battery load tested and go from there.
Ken