Tracking down a short

Yea, I'm going with a current measurement here too. You're looking for a current draw, probably in the mid milli-amp range if it's draining a battery fairly quickly. I would expect micro-amps or low milli-amps of current to be flowing in the "keep alive" circuits.

I recently worked on a VW which had the same problem. It turned out to be a leaky diode in the alternator drawing current and draining the battery after about 3 days. A new alternator fixed the problem.