Yamaha 90 TLRD engine shows overheat warning even when cold. Temp sensor OK

I have a 2005 Yamaha 90 TLRD engine with Analog gauge set. The tach has two warning indicators, low oil and overheat lights. The overheat light comes on as soon as the ignition switch is turned on but no buzzer sounds. The engine goes into emergency mode so only revs to about 2k rpm but otherwise runs fine. I have checked the temperature sensor with an ohmmeter and even disconnected it but the same situation occurs. Is there any other situation that can cause this light to come on even though the buzzer doesn't sound? I replaced the water pump (even though it was OK) but I pretty much know that is not the problem since the light is on even when the engine is cold. Is there some fuse that I need to check ?

I reckon bad ground. When you tested sensor did you also test its feed?

Thank you very much for the reply. Since the temperature sensor seems to be just an open/closed switch, I am not sure how I would check the feed to the sensor. I only see two wires which I assume would not normally have voltage on them since it seems they would only be carrying the current to check for an open or closed circuit. Are you recommending that I check that circuit to see if there is a fault or grounding? I believe the normal state of the temperature is an open circuit (if not overheat has occurred). It also seems strange that I have an indicator light on with no buzzer. Has anyone heard of the gauge itself actually going bad? This isn't a digital gauge, its one of the analog ones (with the white face).