The easiest way to do that is buy a five wire trailer isolator, like this one:
http://wingstuff.com/products/34253-electronically-isolated-trailer-wire-harness?from_search=1
Cut the connectors off the new isolator and cut the 6 pin Deutsch connector off of the BRP 5 to 4 wire isolator. Splice the BRP connector to the input side of the new isolator and a flat five connector to the trailer pigtail of the new isolator. BRP Y harness has a trailer power lead in it that you use to power the new isolator.
To be on the safe side DO NOT wire the trailer directly to the bike harness. If you ever have a short in the trailer wiring you risk screwing up the bike cluster and wiring. The isolator is just that, an isolator. It keeps the trailer power separate from the bike.
I was just wondering. Does the BRP harness that came with the hitch kit have a Deutsch connector between the Y and the adapter? The Y harness I bought for my bike does. I did not buy the BRP 5 to 4 wire adapter. I installed an after market hitch.