OK, just to prove my limited knowledge of electronics, it suddenly dawned on me last night while continuing to ponder the problem, that it doesn't matter that the warning alarm (low volume, turn it off or else) continues to sound - you ain't gonna hear it over the main siren that cuts in 4 seconds later. So I hooked up the main siren, and it works - even from deep inside a Holproof Explorer sock, it works!
INASNT, the little turd didn't want the car, he only wanted the radio, to sell for drugs, probably.
nismoR34 - yeah, tried Jaycar, but they weren't much help, other than being able to confirm that the components seemed to be OK. You get a copy of the review with the kit - it explains how it works, and how to put all the pieces in the right places.