Security alarm goes off sporadically for no reason

Never in 8 years' ownership had my security alarm gone off for no reason until six weeks ago and again last week. The first night (2am; police at my door) a neighbor's car had also gone off for no reason (which is pretty weird), I learned the next day.

NOTHING I did would stop it except to start the engine. As soon as I powered off, however: beep beep beep beep ... again. So I drove it to a deserted area, stopped, locked it, walked 100 feet away, waited a minute or so (by now it's almost 4am) returned to it, started it, drove it home, and there were no beeps for the next five weeks.

Then last week a moving van or the mover's cell phone or both or whatever triggered the alarm. Same resolution except this time, NOTHING stopped the beeping. So I drove it to my Toyota dealer, where, as soon as I powered off, the beeping began and NOTHING would stop it except starting the engine.

GOOD. Now they can fix it.

But NOOOOoooo. It hasn't beeped (or cost me a cent) in over a week. Their only suggestion has been to replace the hood latch and see what happens. No thanks.

This thread (rius alarm goes off for no reason | PriusChat) offered suggestions about checking battery condition and latches. Battery (replaced 2 years ago) is within specs in a link in that thread (to Weird stuff happening? MPGs dropping? Test The Battery | PriusChat).

Latches seem to not be the cause.

What the heck do I do? Bring it back home and hope it doesn't happen again? At least the last time it was 2pm instead of 2am. But I want this fixed.

(I did NOT check the ground wire on the 12V battery because of recent abdominal surgery. If that's an absolute must, I'll do it, but the battery checks fine.)