So I disconnected the minus cable from the battery, and measured between the minus pole and the loose cable.
Low and behold - I saw 12V on my multi meter.
Maybe I'm just dumb, but IMHO - with everything turned off - I shouldn't see any voltage there, or am I missing something?
When you connected the two with your meter, you completed the circuit. Something in that circuit is drawing power. Start disconnecting components, one at a time to isolate the offender.