A cylinder leak down test would be a good idea, especially if you've already got all the stuff to do one, and should confirm some causes of oil consumption. (mechanics.stackexchange.com)
Operation of «most» leak down testers The procedure of operation depends on whether or not you have the cylinder head attached to the engine block or not. (mechanics.stackexchange.com)
It looked like the last battery leaked down on the the starter. (humblemechanic.com)