I do not know how to-do this circuit but I do know that there are relays out there called Timer-Relays and once activated they will burn for a predetermined time.
If you can determine which one you need, you could activate it from the Alarm circuit and it will only still on as long as the timer will allow.
On the other hand Ford has a timer circuit that came in Rangers and it would activate with the door handle or lock, could be setup for an alarm circuit.
I do not know all the vehciles that might have it but my ’95 Ranger XL had it, funny.
Sorry that all I can think of.
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