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, Skid Row Foot Pegs