My switch goes to the brow(cap) lights first, then to the awning. So assuming yours is the same, you will need to hook the new wire to the awning lights after you separate them and make sure you cap off the the existing wires coming from the brows, as they will still be on anytime you turn the brows on. You can test if the original wires go to the brows first, just turn the switch on after you separate the awning lights, brows should come on and awning should be off.
2016 Eagle 293 RKDS
2016 2500HD Double Cab Long Box, 6.0