You're probably going to have to do some digging. Your compressor shouldn't be kicking on when the vehicle is turned off. Main power should be an ignition switched source, hot only when the key is in the on/run position.
You may or may not have a leak. If the compressor kicks on a lot, maybe so. If it just kicks on now and again, that could be nothing more than ambient temperature changes which will affect the pressure in the bags, causing them to dump and/or fill erratically.
When I hook up my toy hauler, which has a very heavy pin, the compressor will cycle on numerous times before settling down. Compressing air causes it to heat up, which raises the pressure. As it cools the pressure drops, and the compressor kicks back on to raise it again. Mine will generally kick on and off 2-3 times after I hook up.