Gas gauge is stuck way past full mark .

Go with Dutch12078 I would say that or a short.

I had a '69 Roadrunner years ago. The speedometer wood always stick on
100mph. I had to bang on the glass hard to make it go down.
Not sure if yours is mechanical...but I'm just saying

Sounds like my 1999 Ford Expedition New purchase to me. Left the dealer with full tank of gas being shown - I thought to myself that was nice of them to fill the tank for me...

I almost made it home before it ran out of gasoline.

Had to get more gas and finally got home with it. When I added gas to the tank the gauge would go down instead of up haha... Took it back to the country dealer and he said they must had reversed the leads on the sensor or something like that. They did have the fuel pump etc replaced which was inside the tank.

He remembered filling up their cars before delivery and noticed my Expedition was already showing full so passed it by haha...

true story...
Roy Ken

I have a 1957 VW right now...when out of gas..flip lever to the right...just remember to flip it back when filling...OR ELSE

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Check for a bad ground or corroded connection at the fuel tank.

Depending on how much it will cost to `fix' the problem you may want to consider what I did back in the 50's when I had my first VW without a gas gauge.
I would keep a little book and make a notation every time I filled up with the date and odometer reading. I would know how many miles I could go before needing to refill and keep an eye on the odometer. In several years using this method I never ran out of fuel.

Sounds like you never need to buy fuel. ;)

I would start at the back of your dash fuel gauge to see if you are receiving a signal from the tank sending unit. Across the two leads going to the gauge, you should read some voltage with the key turned on and zero with the key turned off. If the voltage changes, the sending unit is probably OK. If not, then your problem could be in the sending unit or any of the wiring between the tank and your gauge.
Usually the sending unit is in the top of your tank and can be changed without any fuel spillage, IF you can get access.