DIAGNOSIS Faulty oil pressure sensor or a wiring issue to that sensor. The sensor is a simple switch that grounds when oil pressure is low.
FIX Locate the oil pressure sensor on the side of the engine block. It will have a single wire connector. Unplug it. Start the generator. If the light is off and it runs normally, the sensor is bad and needs replacement.
IF THAT DIDN'T WORK With the wire disconnected, the problem persists. That means the wire is pinched or grounded somewhere between the sensor and the control board. You'll need to trace the wire harness.
HEADS UP Do not ignore this light. Running with actual low oil pressure destroys the engine in minutes. Confirm the sensor is faulty via the test above before assuming it's safe.