Bouncing fuel gauge.
A properly sized capicitor may settle the gauge down if the source is noise on the wires. Its possible that voltage changes that the gauge needle can follow won't be affected much by the capacitor. I would try looking for a loose wire or possibly a dirty connector contact somewhere between where the sender is connected at the tank and the end of the wire at the gauge. Fuel tank senders seem to be affected more in diesel fuel and can sometimes the internal sliding contact can be cleaned. Then there is always replacing either the sender or the gauge with new.
