This could be caused by several different issues. It might be poor ground connections from the battery to the engine; and from the battery to the chassis; or it could be poor grounding of the instrument panel; or it could be a defective fuel level sensor in the gas tank; or it could be a defective fuel gauge; or it could be poor contact in the wiring plugs between the instrument panel and the fuel level sensor in the gas tank; or a poor ground connection from the gas tank to the chassis.
In order to fix this problem; you'll need a good quality digital multimeter, a wiring diagram for this vehicle, and a clear understanding of how to troubleshoot electrical circuits by voltage drop testing.
You can get a wiring diagram from a service manual for this vehicle; either in your local library; or by buying a Haynes or Chilton service manual at a local auto parts store or online.
I would recommend starting by making sure that the battery ground post has two ground leads connected to it; one being the heavy ground cable which should be attached to a bolt that threads directly into the engine. The ground cable cannot be connected to a bracket, or a painted part, or a part that is not made of metal. The second ground lead from the battery should be connected to a nearby clean bolt that threads into the fender. All electrical connections should be polished with a file until they are shiny, on all the cntact surfaces.
When the original ground cable is replaced; the replacement cable often will not have a second ground wire attached. In this situation; a second ground wire must be added. It can be made from a length of 12 gauge stranded electrical wire; with suitably sized ring terminals crimped to the ends; after the insulation at the ends has been stripped off. This wire can be placed on the bolt that tightens the cable clamp; under the nut.
There should also be a dedicated ground wire from a bolt in the engine to a bolt in the firewall. This wire can be fabricated from bult wire and ring terminals if needed. These 2 auxiliary ground cables are essential for proper operation of the electrical system.
I would also locate the ground wire from the fuel tank; and make sure it has not been disconnected or damaged. It is always good practice to disconnect the ground bolt, and thoroughly clean all the wire termnals and the bolt.
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