Had a prod at a power sounder board that still shows signs of life after the battery crud has been cleaned off.
2 12V supplies. Permanent and switched.
7.2V Ni Cd battery (2 x 3.6V)
Battery is charged from the permanent 12V input at a rate of 15mA. Regulated between 14 and 16mA over the range of 10V - 16V input. Above that the charging is cut off. Almost as if there's an overcurrent/voltage protection circuit.
Current pretty much stable down to a short circuit where the NiCd battery should be.
Charging diminishes below 10V input and by 8V there's none, as expected. Alarm sounds below about 6V input, and whenever the power is disconnected. Alarm is silenced when both 12V supplies are restored.
The feed to the sounder (and most of the other circuitry) is fed via a pair of diodes so that it is fed from either the battery or the permanent 12V input, whichever has greatest voltage. Failure of one of these diodes could therefore result in 12V into the rechargeable battery or the rechargeable battery trying to drive the car electrics.
Alarm sounder transformer is indeed driven by what looks like a MOSFET straight from the junction of the 2 diodes. Transformer primary DC resistance is about 1.2 ohms. Feed to the MOSFET comes from a pin on the microcontroller which is toggled up and down to generate the tones.
I hope there isn't a DC path from the microcontroller to the MOSFET as this pin ending up in the wrong state due to a firmware glitch would result in combustion without a doubt.

I must double check the above.
The area around the MOSFET is one of the areas that was affected by battery leakage on this unit.
Kevin