Check the little ground wire comming of the top of the gas tank, it should be secure and wire connector on solid clean metal. The wire should be screwed or bolted to gas tank support brackets or close to that area.
Or if you have the original sender ( looks like a soup can ) the float is stuck, OR check the fuse first. Let us know, good luck.
Gauge should show empty when the wire than feeds the gauge is grounded and full when disconnected. If the needle moves the problem is in the tank not in the instrument wiring or the gauge.
The sending unit is a simple rheostat that goes from 90 (or 30 if your car is old enough) Ohms of resistance to zero (dead short) activated by a float. Your float may have filled with gas and sunk, or you may have gotten water in your tank from condensation that corroded the wires in the sending unit.
I'm having a similar problem where the needle stays at just over 3/4 full unless you unplug the wire coming off the tank, in which case it tags all the way out past full then returns to 3/4 once plugged back in.
Dave: Is this what you meant when you mentioned movement in the needle, or do you mean regular movement as gas is used but maybe just not accurate indication of actual fuel level?