If it's not related to the airbag system, perhaps it is the door chime?
On my '96 Mark VIII, the door chime will come on at times even with the key removed from the ignition. It goes off with the door closed so I haven't bothered to check into it. It's only supposed to come on with the key in the ignition and the door open.
I don't know if the two could be related but I would bet if the door switch on my car went bad, it would chime full time. So, I'm wondering if the door switch in your continental could be faulty along with whatever else is going on and the car simply thinks the door is open? Does the chime sound like the same as when the door is open and the key is left in the ignition?