That was interesting.....
So, I ran a wire into the plug where the instructions indicate for the ground wire (and where I am missing a wire coming out of that plug). The sensor powered up just fine off of that; the LED lit up, and also the security light in the dashboard did the same thing where it was minimally lighted. But, when I locked the door the sensor didn't work! It seems that that line is not active when the door is closed for some reason. I put it back as it was, and it works still (with the extra "feature" of the dimly illuminated security light and occasionally flashing dome lights).
Da 6, that might have been your problem...if you never got it sensitive enough then it might have been powered down like I saw. The sensitivity test is to drop a tennis ball on the windshield, and the alarm goes off when I have it turned about 1/3 of the way around and do that.
I'm going to try running the ground wire to some metal and see if that changes things. I'm starting to think that the instructions aren't valid for the Mazdaspeed 6, or that the wire that it pointed me to for the accessory power isn't the right one (though it's the only orange one I see). The alarm works, I'd just like to get the wiring so that it doesn't do this strange glitching before I write it up.