Hello & welcome to AF! I scanned the info you need on the alarm system, from the 92 Owners manual. Click on the thumbnail to expand. You may have a bad "tamper switch" on one of the doors or trunk lock. The tamper switch detects unwanted guest from jerking or otherwise trying to disable your locks without a key. In the trunk, you have a blue wire coming from the "tamper switch" and it can be cut to disable the switch. This would have no effect on opening & closing of the trunk! It only disables the tamper switch. Of course, it you want to replace the switch, you can get a new one from the dealer for about 100 bucks. You might find an owners manual on Ebay or at a salvage yard. It sounds like you inherited a nice car!
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Merry Christmas!