I don’t have a circuit diagram to hand but if you think about this logically.
When the engine is not running and the key turned on, the safety circuits are activated. There is no lub oil pressure as the engine is not running. The engine lub oil light will be straight from a pressure sensor on the back end of the mechanical oil pump, therefore would be on. The alarm sound, which is probably common for overheating , (but not sure about that) is disabled during engine run up to avoid the alarm sounding until oil pressure is reached. This in most cases is achieved via the Tacho signal, so alarm will be held off until a certain revs are reached, by which time oil pressure should be achieved. This is the normal procedure for any basic comustion engine. So it looks to me as though this is not functioning. Providing the light is going off and the alarm stops when the engine starts, then the oil pressure is fine and not a concern . I’ll have a look next time I'm at the boat and try to figure it out.