2009 Dodge Ram 1500 - Suggestions on a key-related battery dead?

I use my 2009 Ram 1500 with the 5.7 Hemi to pull a 24 enclosed car trailer however I have not used it in a while although I have been starting the truck on a regular basis. A couple of months ago I started it and let it run for a while but when I turned off the switch the engine kept running. By wiggling the key I was finally able to shut it off. A couple of weeks ago I went to start it and the battery was dead and would not take a charge. A new battery was installed an the truck started. Every thing seemed fine but when I shut it off the engine kept running even with the key removed. Before I spend $195/hour at the dealer what is your diagnosis?

Anytime someone mentions electrical gremlins in a Fiat/Chrysler product, the first thing that comes to mind is the TIPM.

Tester

Do you have any aftermarket additions? Crazy story GMC van, installed a powerpoint for the rear of the van for a spotlight, tapped into ignition controlled 2 way radio power source. If the light was plugged in the van would not turn off.

No aftermarket additions, everything factory installed (towing package, etc.)

I’m still grappling with pulling a 24 car trailer with a pickup truck.

My guess would be a bad ignition switch.