If your vehicle is showing fuel gauge stuck on full or empty, here are the most likely causes and the parts you'll need to fix each one.
The variable resistor track on the sending unit wears out over time, or the float loses buoyancy, causing the gauge to read incorrectly or get permanently stuck.
If the fuel pump was recently replaced, the delicate float arm may have been bent or positioned against the side of the tank during installation, physically preventing it from moving.
A broken wire, corroded connector, or bad ground between the fuel tank and the dashboard can cause an open or short circuit, pegging the gauge to full or empty.
The tiny stepper motor that physically moves the fuel gauge needle can fail, or the cluster's internal circuit board may develop bad solder joints.
In modern vehicles, the fuel sender data is processed by the BCM before being sent to the gauge. A glitch or failure here can cause incorrect gauge readings.