Hello,
I'm searching back in my memory quite a ways, so forgive me if I'm mistaken, but I believe the problem you are having with your alarm is a malfunctioning tow-off sensor. These were originally installed to set off the alarm if the car was lifted with a tow truck or a flat bed. It is white in color and should be located under the rear seat on the driver's side. Just unplug it. I was a factory tech from 87 to 94 and can tell you that this does not interfere with the operation of the alarm in any other way. Hope this helps.
Mike H.