I had this happen not long ago when fuel tank was low on gas & in my particular case, it was fixed as follows:.
1. Got 2 wires from 2 coat hangers & removed the gas tank cap.
2. Shaped the end of one wire to look like a fish hook, to pull the gas gage wire upwards.
3. Shaped the other coat hanger wire to look like the alphabet letter W, (or sideways S), to push the gas gauge wire downwards.
4. Pulled the gas gage wire up & pushed it down repeatedly to wear away the sticky varnish, rust, or whatever deleterious material was preventing the gas gauge from moving freely.
5. Filled tank gas plus with 4 ounces of Marvel Mystery Oil.
6. Now have the happiest gas gauge in town.