Bill, Hi.
Replace the fuel gauge. All mechanical fuel gauges have, lets say a brake?, that keeps the needle stiff so that it doesn't flip back and forth as the gas sloshes around in the tank which is what yours is doing now it sounds like to me. I've got the same issue with the gauge in my '75 chevy pickup. As the needle moves from full to empty and back over many years, it wears the little brake out. You probably notice that needle flips less when the tank is completely full as opposed to half a tank or less due to less room for sloshing.
Good luck, I hope this helps.
T.A.J.