Does the guage stay at the same spot when the car is on to when its off, or does it just not drop all the way when off?
Does the guage read true, ie full when full empty when empty, etc?

Its a bit hard to really diagnose, but i would be looking for persistant power somewhere first.
After that, look for bad earths, or add eatra ones at the fuel tank and at the dash.

If thats not successful, the sender could be playing up. ie showing 1/2 full when empty or something like that.

After that, its a test light, multi meter and lots of paitence.