I had the same question about by Jeep. I planned to install another brake switch so the light could be powered with the battery neg terminal disconnected. The battery switch I bought had a bypass wire and fuse that allowed this arrangement.
I gave SMI a call. They suggested a vacuum switch rather than another brake switch. For about $40, they can supply it or your local NAPA may have them. With the same battery switch and the bypass wire/fuse, you can power the AFO and the vacuum switch and the LEDs from the car battery even when the neg terminal is disconnected from the car (BTW, in normal operation, the AFO consumes no power other than what the LEDs want, so there shouldn't be any battery drain issue. I drove three days without running the Jeep's engine and, on the fourth day, it cranked right up).
My solution was, based on a lot of experience from the gang at IRV2 concerning towing issues on Jeeps, I do not disconnect the battery. I just completed a 4000 mile trip with no apparant ill effects (no engine/trans issues, no odometer incrementing, etc.). But, I really don't know about the Dodge.
Give SMI a call and keep refreshing your post until some Dodge owners chime in.
About the indicator LEDs. SMI suggests you mount the assembly on the tow bar. I mounted it temporarily to check it out. I really want to be looking at the back of the Jeep as I'm tooling on down the road, not at the tow bar. So, I made up an arrangement to clip the LEDs to the rear view mirror. It worked better that the tow bar, but in some lighting conditions, it was difficult to be sure the light was on/off when appropriate. I decided there's nothing like another light on (or near) the dash. I plan to add that before the next trip.
'07 Bounder Diesel 38N
'08 Jeep Liberty Pusher