You've got it basically right about disconnecting one circuit at a time but you don't need to wait for the battery to run down. A simple multi-meter will tell you instantly if there's a current draw. If you have current flowing on a circuit with everything off then check the individual components on that circuit the same way.

Save a life, adopt a senior shelter pet.
The three main causes of blindness: Cataracts, Politics, Religion.
Name your dog Naked so you can walk Naked in the park.