Could be more issues aswell but when the alarm does not arm it will draw more current then if it was armed. The security light is supposed to light solid after shutting the doors and locking them. It will light solid for about 30 seconds(sorry, never timed it) and then the light will go off. It is not supposed to keep blinking...that tells you it has not armed because one of the door/hood/hatch pins or locks are not engaged. The fsm has a section on troubleshooting the alarm. I was able to find and fix my driver side lock when my alarm started to flash continuously like yours by using the fsm.
