Hello and welcome to justanswer.
This is a fairly common problem in the Rodeo. Replacing the fuel level sensor in the tank should fix the problem. The tank does need to come out of the vehicle for this repair.
Please let me know if you need additional information.
Since the check engine light is on as well, the problem is between the fuel level sensor and the engine control computer (PCM). The wiring will need to be carefully checked. The best way to check the wiring would be with an ohmmeter. Check for continuity between the fuel level sensor and the PCM. Testing resistance across the blue/yellow and orange/green wires at the PCM connectors will verify integrity of the circuit. I have included the wiring diagram for you below.
Locate and unplug the red connector (E22) on the PCM (under the hood on drivers side fenderwell)
Then test resistance with an ohmmeter across terminals 50 (orange/green wire) and 60 (blue/yellow wire) If you get an open reading, the wiring will need to be repaired. If you get a reading between 0-200 ohms, the circuit is good and the problem would then be in the PCM.