Just a couple of further thoughts; firstly as you say with the key out the circuit should be closed- but as there's a fault somewhere that's draining the battery I'd want to prove it is closed-first pull the multiplug off the bottom of the keyswitch, then retest, then pull the multiplug of the recitifer and retest, maybe one of the diodes in there is going & it's open through that.
(by the way, I think Lloyd's onto something about the pulsing, most multimeters don't poll the reading too often either)
Oh, one other thing, you haven't got an alarm fitted, have you...?