On my '88, you need to unlock the passenger side door to disable the alarm. I have a blinking light on the right side of the dash for the alarm. It goes solid when I first lock it up, then blinks slowly after a couple of minutes. If yours remains solid, the alarm circuit may be in trouble, and you may have to by-pass the starter cut-out circuit. Check out his thread if that is the case:
http://www.toyota-supra.info/forums/...rm-system.html