If your KJ did NOT come with an EVIC from the factory you have to purchase the "supplemental harness" to complete the install.
I never did figure out why the additional harness is necessary but my KJ didn't come with an overhead EVIC from the factory nor with a hitch or trailer harness. I bought both harnesses and installed them per the instructions and all lights work.
The supplemental harness has additional power wires that plug into the power outlet next to the cubby in front of the shifter as well as the extra wire for the brake controller. Like I said, I never figured out how the KJ harness with the EVIC differed from a non-EVIC KJ but my guess is the the supplemental harness added power to the 7-pin - including the running lights.
The price is cheaper than when I bought mine a few years ago - I found this on the web:
Supplemental Harness - Trailer Package
Bob