I wish I had found this thread a week ago. I had exactly the same problem, -12 reading only 1v or so, some mystical low-ohm reading between -12 and ground even with every cap that could have shorted removed. Then I found the bad cap on 3.5, same carbon buildup, bingo. I sure spent a lot of time tracing, removing, replacing. At least it was educational. BTW, my final diagnostic tool was to use a delicate procedure... back-feed the -12 with a bench supply capable of supplying 5A at 12v and waited to see what caught on fire, or at least got hot. Seconds later, that pesky cap identified.
Bill