Sounds like an intermitent short to ground somewhere between the sender and the gauge. I just researched the pegged at 3 problem with the help of this board. My problem is a bad sender. If I remember correctly you should bypass the wiring and jumper from the sender to the input at the instrument cluster. If this clears the problem you would indeed have a short to ground that comes and goes, maybe a chaffed wire. Also, could be the sender is failing and is not completely dead yet. Seems to be a very common problem.
Harold