Anti-Theft System Issue?

[philcindySC300]

I am an SC300 owner. I have had this car 3 weeks. 1993 with 42,000 miles. I am not sure if the theft system is working right. There is a security light on the dash but the button on the key does not activate it but it does lock and unlock the doors. Yesterday as I shut off the car and pulled the key, I heard a series of chimes that after a few seconds, they shut off. then today I stopped at the mailbox, pulled the key and heard the chimes again. When I got back in the car it started but as I pulled into the driveway the whole car shut off dead. I could not even close the sunroof. Battery power was up at normal and went through the normal reset procedures with locking and unlocking with the key and even pulling pos cable from the battery, all to no avail. After about 10 min leaving it alone, I went out and started the car like normal. Logic indicates that the anti theft system is the culprit. I have no manual yet,( one has been ordered)so I am mystified as to how all this works or doesnt. I plan on an aftermarket alarm system as I only have 1 master key. That will allow me to make 2 duplicates and leave the master key at home. Is this the correct way this should function or is there a bypass or kill switch I can disable? The new alarm will go in next couple of weeks but I need a solution. Rest of the car is beautiful and I know I made a good choice for my first Lexus.