JK's are controlled almost completely computer controlled. They communicate through a system/protocol called CANBUS.
I hate to sound negative, but enough strange symptoms typically isn't just 'coincidence' ...
You can try removing the terminals, both of them.
I'm not sure if I would personally go this route, but after you've disconnected the leads from the terminals, you can touch the leads/wires to each other. All this does is act as a direct short to remove any stored electricity in capacitors. I hope there's someone who can do a better job of explaining this than I, but by completely removing all the electricity from the system - anything that isn't hard memory would be lost. In this case, that's exactly the state you want to get back to - original.
If at the original state, you still experience symptoms - you have a more significant issue. See the dealer.
There is always a change that data wires were damaged & that's the cause. Without the proper tools, that can be a great task - track down a pinched/shorted/cut data wire. You can't test data lines for voltage. You can check if they're live or not, buts very difficult to trigger the fluctuations in voltage you might need to test the circuit.
All I would try at this point is to disconnect the negative terminal, let it sit for 15 min or so. Reconnect.if problem persists, see the dealer if you decide it's driving you nuts.
p.s. while a needle in a haystack is always fun, if you have the time, you can always pull carpet & dash looking for damaged data lines. There's no tests needed when you can visibly see a damaged wire ... Best of luck !!