If its truly jumping around and not whats refered to as humming bird, then you simply need a new fuel level sender, if its doing the humming bird thing it has nothing to do with the sender.
Humming bird fuel gauge is quite normal and has nothing to do with the pump or sending unit. The fuel gauge on the 96-99 chevys is analog but the system is odd, analog signal goes to the computer, then the computer sends a digital pulsed signal to the gauge. The gauge over time loses the dampening fluid from inside the gauge allowing it to show the pulsed signal as a flutter/vibration. There are several places online that show replacing the silicon dampner fluid, it will leak again. My plan is to try bypassing the computer so the gauge sees the level signal directly. I haven't done it yet as the gauge flutter is pretty far down my list of things I need done as it still displays correctly, just has humming bird flutter.