Hi Nick,
My boat’s home is just around the corner at T-Bird Marina. I think your Yamaha 30 is similar to a Yamaha 25 where the motor is mounted under the V-berth and you probably have an YSM-12.
Based on your description, I suspect there is an intermittent wiring problem in the alarm circuit. Check the wiring harness and sensor connections. The alarm circuits are described in my YSM-12 manual in Chapter 11 (electrical) Section 5, starting on page 11-22. The Temperature and Oil pressure sensors are normally open and close (connect to the engine ground) when high temperature or low oil pressure is sensed.
This in not how to design a failsafe system but that is how they were made. If you have the original alternator, the charge alarm is activated when the alternator sense terminal “L” voltage is less then the battery voltage. The alarm buzzer will come on when ever anyone of the three alarms lights are on.
You should be able to trouble shoot it without running the motor. The oil and charge lights should come ON along with the buzzer when you turn on the key switch. Locate the oil sensor and pull off the connector and the low oil lamp should go OFF. Locate and ground the water temperature sensor and the high temperature lamp should go ON. The charge light is more difficult to check and you have to be careful not to short or open circuit the alternator or the internal voltage regulator or diodes may be damaged. Read the manual. I can email you a copy if you don’t have one.
The key switch only enables the starter switch and the alarm circuit. I strongly recommend that you never operate the motor without the key switch ON or the alarm circuit will be disabled and you would not know if the motor overheats or looses lubricating oil and can result in destroying the motor.