If the oil light goes out and there is a steady alarm, then you have an oil pressure problem. The green oil pressure light being on indicates oil pressure is good.
The only other thing that creates a steady alarm is an overheat or it thinks it is overheating.
Your impeller could be weak and need changing.
Your thermostat may not be opening all the way.
Your cooling system has a partial block.
Your overheat sensor is bad.
or you have a wiring issue causing the warning horn to blow. This may not light the red overheat light.
You should also have a red light, indicating an overheat. Your light could be defective.
Lots of possibilities.
Mike