Ignition cut-off switch

Years ago I had an alarm system installed in my 1988 Vanden Plas. The alarm system is designed so that the car will not crank and start when it is armed. With the alarm off I am now experiencing, on occasion, no crank when the key is turned. The car eventually cranks, but only after several turns of the key and usually many minutes later. I have replaced the starter relay, added an additional ground strap to the chassis, and ruled out the Park/Neutral position inhibitor. Before I consider replacing the ignition switch I would like to check the alarm connection to the ignition cut-off to see if that is the culprit. Where do you suggest that I look to find the connection?
Thanks.