bad sender connection
Look at the wiring on top of the fuel tank at the sender. It tends to get dirty and corroded up there, but there's no way to clean it from outside.
Fortunately, there is a access hatch under the rear carpet to get at the connection and clean the green corrosion off the tabs.
Just remove the rear carpet trim molding. Roll up carpet, remove 2 phillips screws on access panel. Pry up panel. Sometimes it is very stuck to the weatherstripping.
You will see the wires to the sender unit now. Remove connector, clean connection with sandpaper, emory board, x-acto knife, whatever... Blow it clean w/ brake cleaner and compressed air. Reconnect, turn key to run position, watch fuel gage.
If gage still doesn't work, repeat as necessary.