Fuel Gauge question...

[tsubaki]

The back of the gauge (most of them) have terminals S = sender, I = 12 volt positive and G = 12 volt negetive.
The two wires going to the sender are connected to G & S.
If you have 12 volts between I & G and remove the wire at the S terminal and the gauge dosen't go to "empty" then it is the gauge.

[tsubaki]

Sounds like the sender.
Unplug and unbolt the wires at the sender to see if it does go to "empty", just in case there is a pinched wire or corrosion.

[tsubaki]

The senders are nothing but a rheostat.
Some can wear like sandpaper and read intermittently, completely lose contact and not read at all or stick at any given location and read a constant value.

I don't remember what the resistance values were on those things.
Like spare said: "Take the sender out and hook an ohm meter to it, slowly run the float up and down, it should change the ohm reading in a smooth flow, any jumps or zero readings would indicate a bad sender", as would one reading a constant value while moving the float up and down.