It looks like a solenoid relay, like on an aircraft master switch or motorhome disconnect. I had a neighbor that had a MH with a latching relay for both coach and chassis, one of them was sticky and needed several cycles of the rocker switch to either get it to turn off or turn on, can't remember. Took it apart and cleaned everything up and it worked properly again. If you have one of those, without an annunciator light to show the status it could be remaining on and causing the drain. That would also be why it would start in either position.