Your trailer will have either a 4-pin, 5-pin, or a 7-pin plug. Do you know which you have on your trailer? The 4-pin is the standard, it just covers running/brake lights. The 5-pin is more commonly used by boats as the additional pin is for the reverse lights that locks a hydraulic brake while backing. A 7-pin is used if you have a brake controller installed. They make adapters for your vehicle to step down from 7-pin to 4 or 5.
Most RVs and larger trailers will come with electric trailer brakes and and you should then install a brake controller and the additional wiring harness for that controller. The wiring harness you have is not for electric brakes.
Hope that helps.
2011 JKU Sahara, Sahara Tan, Leather, 3.73, Auto, Hard/Soft Top, SpiderWebShade, Dead Pedal
Coming soon: 2013 Rubi 10a Wheels, New Tires