I would assume pretty sure its a " resistance " fuel gauge.. so check your wires to make sure there's excellent contacts and none are cracked or broken ( just hanging on) also you can pull the sending unit out an check its hmm i think ohm resistance .. ( someone correct me if i'm wrong ). as the float rises it changes the resistance up or down, an that's when you see the meter move in regards to it. Short of that depending on how old it is you may just want to change the sending unit and re wire it. I haven't done it ( did on in my '70 cougar) in my F series but i'm sure is the same or just as easy.. hope this helps.
Any other opinions out there?