here is a reponse i got from a ford tech on disabling the factory alarm.
"looking into your problem and if that trunk tamper pin or open/close sensor is messed up that will cause your problem. After looking at the wiring for the alarm, the module needs to see inputs from both front doors and the trunk after it is armed. If one is messed with or the ground isn't there for one of those it will go off. You can also disable your factory alarm and still use the unlock/lock on your fob. The module is in the trunk on the left side and it has a natural color connector. If you look at the connector with 6 pins on top and 7 pins on bottom, you want to take away the second and third pin on the bottom counting from the left. The second pin is actually #6 and is for the doors, and the third pin is actually #5 and is for the trunk. All those other pins are for your lights, horn, and all the other stuff that goes off when the alarm ringing. You could probaly just unplug it too, I don't see that causing a problem either. Hope this helps. "