The fuel gauge sending unit is a variable resistor.
Pull the sending unit, and remove the outer tube.
Inside are two parallel wires with a wiper on a float that connects the two wire. These wires oxidize and will create an intermittent connection.
Use some very fine sandpaper and gently wipe down each wire where the wiper makes contact with the wires.
I had the same problem and the fix was as describe above. The displayed level no longer jumps around... but I use the fuel gauge as a low I.Q. suggestion. When I get to 200 miles on the odometer, I fill up.
