Dan...
Thanks for asking the question. I'm also in the process of towing my 2011 Wrangler. I appreciated the one answer you got regarding why the key needs to be on. I can't figure out the logic, but as mentioned the owners manual is clear and Auburn Jeep says it has to be on. They can't tell my why, they just say it has to be on.
Have you figured out your brake assist yet? Our used motorhome came with a "Brake Buddy" with lots of attachments and several pages of instructions on how to hook it up and trouble shoot. It needs the jeeps battery, so that's been my first challenge. In the process, I've talked to several RV'ers and have gotten different answers from most. I know in California, and several other states, brake assist systems are not required for our jeep. In Canada, and probably some states, they are required. I've come to the conclusion they are probably a good idea, but not a requirement. What have you decided to do? I'm also using a Blue Ox system.
Bill