I just installed the Brandmotion 9002-8837 in my stock 17 JKU Hard Rock and had the same problem: put in reverse and screen goes blank with "Check entire surroundings" on the screen. I called Brandmotion customer support and the issue was I incorrectly installed the power. Customer support said if the radio 430N screen goes blank in reverse, the computer is properly flashed, but the camera power isn't correct. Here's what I did to solve the problem: I connected the camera's Red wire to the Jeep using the Quadratec 12v Power Adapter. The camera's black wire was put on one of the three grounding terminals on the passenger-side kick plate. The camera green wire (the trigger wire) is spliced into the reverse light wire (white wire with grey stripe) located in the wiring harness under the passenger side kick panel. To do the splice, I went to AutoZone and bought a "quick splice" clamp for $2.
Photos are attached.
This was my first time wiring anything in my JKU, and I'm very inexperienced with wiring. But, my camera now works flawlessly!

The plastic connector is the Quadratec 12V power adapter. It connects directly to the cigarette plug. Insert the camera red wire into the adapter.

This is the '17 JKU Hard Rock wiring harness in the passenger side kick panel. The white wire with the grey stripe(left side) is the reverse wire

This is the rear tail light wiring harness with the same white wire with the grey stripe (the reverse wire)

The "quick splice"

Finished quick splice on the passenger side wiring harness. Quick splice attached to the white/grey wire and the camera's green trigger wire (Insert both wires before closing the quick splice clamp).

 

It's been my experience that this type of connector has little corrosion resistance. Too much exposure to moisture/salts can make the electrical connection fail. My preference is to solder.