fuel tank gas gauge is constantly moving from full to empty?

Hello,

Sounds like either the fuel sending unit in the fuel pump is defective or the gauge cluster is faulty.
Do you have issue with any other gauges? or just the Fuel level gauge?
If that is the case then it is more likely the fuel sending unit. Which has a float that tells the amount of fuel in the tank.

Here is a helpful article:

https://www.2carpros.com/articles/how-to-replace-an-electric-fuel-pump

I have also attached replacement procedure for the sending unit.

Let me know if you have any questions.

Thank you.