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Hi. One idea is that I know on your Towncar the alarm also monitors the door ajar switch inputs.
You need a scan tool to monitor is one of the switches is reading ajar when it should not be. At anytime when you use the car does a door ajar warning come on?
If there are no door ajar warnings then I would suspect the switches are working. The alarm also monitors the drivers door lock cylinder with a switch. So there can be an issue with that switch.
This here is the procedure to disarm the system. This procedure and others I have are from the Ford workshop manual. Perhaps what you should try is to connect all the switches again. Then perform this disarming procedure while the vehicle is locked and the alarm is not going off. Perhaps this will keep your alarm from going off again.
Disarming an Untriggered System
Also CLICK HERE for the alarm description and operation. This will explain how the alarm works and the inputs it sees to trigger the alarm.