fuel gauge improper reading reads full when empty gage moves back and forth on a

most of the time when this happens,it is a bad fuel sender, switch/float.it is part of the fuel pump module assembly located in the fuel tank.its job is to let you know how much fuel you have in your tank.it sends a signal to the fuel guage.the pump is still working,because you are still driving it.the only way to fix it is to replace the whole fuel pump module assembly,which requires the removal of the fuel tank.the assembly is around $300.00 if you do it yourself!another option,set your trip button on the odometer to 0,go fill it up.if you get 400 miles to the tank full,and you put 300 miles on it,go fill it up again and reset trip again to 0.

Maybe float