Warning alarm does not sound when I start the motor

[capttwb136]

I have a 2003 60 Merc outboard, the warning buzzer does not sound when I start the motor. I grounded the alarm wire in the motor and the alarm sounds so I know the alarm itself works. However it does not sound when I start the motor. I'm afraid to run it with the alarm disabled for fear of overheating the motor should the cooling intake get clogged or it isn't getting oil. I searched the forums, it was not there. I believe the previous owner disabled the alarm. It had a bad thermostat when I checked it because of a weak pee hole flow, but they had put in a new impeller. So that tells me they had a problem and the alarm sounded and the impeller did not solve the problem because it was actually the thermostat. Anyone know anything about the warning alarm system?