A Yahoo Previa Group repost, but it's me, so I can respond to this thread. In case it's useful...

Does your alarm go off when you unlock the driver's side door with the key? It may be a faulty switch at the end of the lock cylinder that doesn't detect that the door has actually been unlocked.

Unfortunately, as with many things Previa, there are multiple steps to get at it.

The minimum you need to remove (on a 1992 with no remote) is:
  • Upper door trim panel (2 screws - door handle and middle bottom, then pull out from clips at bottom and pull up to get "lip" off door sill)
  • Rods connected to inside manual door lock and door handle
  • Plastic cover over access panel
  • Rear window guide rail (unscrew at bottom, tab-in-slot at top)
  • 3 screws holding on door handle
  • Partially pull out door handle
  • 2 control rod connections at door handle and end of lock cylinder
  • Wire "C"-clip holding lock cylinder in handle (pull up)
  • Remove door handle (tilt out from back)for room to examine lock switch

The lock cylinder has a slot at the end that engages the switch. When the
contacts inside become filthy and/or corroded enough, the contact at the bottom
doesn't always conduct, the unlocked door still looks locked to the system when
you open it, and the alarm goes off until you re-lock and unlock with the key
and eventually contact is made on one of those tries.

The harness and connector are a nuisance to remove - the more
electrically-confident might choose to clip off and solder a new switch on
at the door handle opening (I'd do that next time).