Links to the 1991 service manual are in the NSX Prime Library (red banner at top of web page). The electrical section of the service manual covers the alarm system and should provide you with everything you need ot know to fix the problem or disconnect the system.
By any chance do you have a duplicate aftermarket security system installed? If so, I would look there first. Based upon the anecdotal evidence from posts on Prime, the failure rate on aftermarket systems is >>> higher than the OEM system.