This is a shot in the dark, Is it possible that the vibration possibly from a bad U-Joint shakes enough to vibrate the sender for the tank maybe shakeing somthing loose?
If you feel the shake in the seat of your pants it's in the rear if you feel it in the wheel it's in the front.
I would start with dropping the drive shaft and check the u-joint's then the endplay in the pinion(move yoke in and out} yoke should not move. If all that looks good swap rear and front tires see if problem moves.If it does it's in your tires.

If you truly have a fuel problem check your plugs they will tell the story. If it's a carburated vehicle check the fuelpump sometimes they pump fuel into the crank case when they go bad. That is if it's a Mechanical pump mounted on the engine.
Thats all the basic stuff I can think of.

Good luck!