2000 cougar/alarm false alarms?

Did a Google search and found nothing. Sorry if this is an FAQ.

My 2000 V6 Cougar is (aparrently) a stillbirth.

The 1st 3 years, it was in the shop more than it was out. Google my
name in this group to see what a POS it was.

The next 3 years, it seemed reasonably reliable. That changed last week.

About 1 time out of 3-5, when I get into the car, sometimes when I get
in and sometimes when I turn the ignition, the alarm "kind of" goes off.
.... It gives this little half-hearted "beep-beep."

I've found that stepping out, locking the door (via the door switch) and
walking, with the keys, out of range for the car to see them, then
coming back and stating it again, thusfar, fixes it for the time being.

I've replaced the key battery=--no help.

I've had my dealer replace the "module" (whatever that is)--no help.

Anyone have any idea how to solve this? Preferably without making yet
another one of my dealer's kid's dental payments?

Many thanx!