As a Jeep owner (an older one), get used to chasing electrical gremlins now and just put a battery kill switch on it. :)

Amusingly, you can and probably SHOULD lock a doorless wrangler. On a JL and even on the JK, the alarm system still locks out some functionality. And most people don't take the tailgate off, which when locked, kinda keeps people from getting at the little compartment under the cargo floor. It's not really an effective safe place, but just a neat thing.

You can also put a lock on the hood, which is a good idea since that way nobody can disable the security system lol.

Edit: Also of note, the JL wrangler uses an RFID chip for the ignition startup itself. It's separate from the rest of the keyless go system.

Could rig up a switch somewhere inside the car near the driver's seat pretty easily. I had an old motorcycle with some kind of electrical issue that would drain the battery if I left it off for more than a day at a time.

But instead of spending days and weeks chasing it down, I spent maybe $30 on a battery cover with a little hidden flip switch. It was originally designed for turning on (illegal in my state)under lights, but I modified it slightly and had the switch connected to the ground terminal instead, so whenever I got off the bike I'd flip the switch and boom, problem solved, no more dead bike.