Bouncy gauge is not caused by the sender. The reading "damping" (why it doesn't fluctuate quickly as you accelerate, corner, up or downhill, hit bumps, etc) is handled in the gauge itself. The float always moves, very easily, and the only reason you don't see that movement constantly is that the reaction/interpretation of the float/rheostat in the tank is slowed down by the gauge. This is also why the GM manual states that you need to give the gauge time to respond when testing the fuel gauge circuit operation. There are no electrical components (carbed gas engine) on the sender other than the rheostat that is actuated by the float.
Even grounding or breaking the ground of the gauge sender wire does not peg a fuel gauge instantly, given that everything is working correctly in the first place.
Now of course, as soon as you make an authoritative statement like that, for some reason or another it will turn out to not be true.

However, there are likely other issues as well, the fuel tank gauge circuit is a common "failure point" in these trucks.
But, even if you pull the sender, you can likely clean it up. Never hurts to touch up the sender ground either.