Here's a breakdown of the possibilities:
* Faulty Fuel Gauge Sending Unit: This is the most common culprit. The sending unit is a float inside the fuel tank that moves with the fuel level and sends a signal to the gauge. If the sending unit is malfunctioning, it might not be sending an accurate reading, or any reading at all. It also could be the sending unit isn't properly grounded or has a wiring issue in the tank itself. This means the gauge is wrong, but the light might still work (or not).
* Wiring Issues: A break or short in the wiring between the sending unit and the gauge, or a bad connection, could prevent the gauge from reading correctly. The low fuel light might use a separate circuit or have a different trigger point (it might be set to a lower fuel level than the gauge's empty marker).
* Instrument Cluster Problem: This is less likely but possible. A fault within the instrument cluster itself could prevent the gauge from working accurately while leaving the light operational. This is more likely if *other* gauges in your cluster are also malfunctioning.
What to do:
1. Don't risk running out of gas: The gauge is clearly inaccurate, so fill your tank immediately. Running out of gas can damage the fuel pump.
2. Check the Fuel Gauge Wiring: If you're comfortable working on cars, you could try tracing the wiring from the sending unit to the gauge. Look for any obvious breaks, corrosion, or loose connections. This will likely require accessing the wiring under the back seat or near the fuel tank, so it may be best to leave this to a mechanic if unfamiliar.
3. Replace the Fuel Gauge Sending Unit: This is the most likely fix and usually involves dropping the fuel tank (a more involved repair). A mechanic will likely need to do this, as improper handling of the fuel system could be dangerous.
4. Test the Gauge and Light Circuitry: This is best left to a mechanic with diagnostic tools who can test the voltage and continuity of the fuel gauge and low fuel light circuits to determine the exact location of the fault.
In short, don't rely on the inaccurate gauge. Fill up your tank and get it checked by a mechanic to diagnose and fix the underlying problem to prevent being stranded with an empty tank.