I tried something I read on cars101.com.
I got into the car and closed the doors, waited until the starting lights went out,
then I held my finger on the lock/unlock button, holding it down in the unlock position, as I
put the key in the ignition switch and turned it to the On position, still holding the button down, then quickly, before a second had passed, opened the door, still holding the button down until I heard the horn beep, then I released the button.
After that it wouldn’t blink like it was (rapidly) except right after I got out, locked the door and locked the car with the fob, setting the alarm, after which for half a minute it would blink continuously. , then set it to a double flash every few seconds.
I tested the alarm by not disarming the alarm with the fob, then opening the door with the key, at that time, the alarm went off.
I’ve noticed now that if I go out and lock the doors and don’t set the alarm, the security light flashes every few seconds.
Now, I think, if this is fixed, I can tell by looking at the security indicator on the dash if the alarm is set (doulbe blinky) or not set (single blinky). Maybe, I’m still looking into it.