From the FSM ....
"Passive arming occurs upon normal vehicle exit (open door, lock with power locks, close door). The Security lamp in the panel will flash for 15 seconds, indicating that arming is in progress. Note that this 15 second arming period will start after the Illuminated Entry has timed out (courtesy lamps off). If no monitored systems are activated during this period, the system will arm. If the hood switch is not seen by the system, the Security lamp will remain steadily lit during the arming process, although the system will still arm."
"Passive disarming occurs upon normal vehicle entry (unlocking either door with the key). This disarming will also hault the alarm once it has been activated."
"Upon initial installation (connection to battery), the Vehicle Theft Security System enters its power up alarm mode which flashes the headlamps, park and tail lamps, and prevents the engine from running. To exit this mode, the system must be disarmed as mentioned previsously".
"The alarm system will not arm if the doors are manually locked, providing a manual override of alarm."
BTW: I'm curious ... was it like this when you bought it or did you inadvertanly activate the alarm after driving it home? If it's the latter you literally stole this one for $300 bucks!
If you have more trouble let me know... I can scan the entire section in the FSM and send you a PDF.