granted im not the best at wiring but i know a little. i wired it in like the factory light and it didnt work. so i checked with another website and they told me to use a 12 volt relay and i hook it up like they said and i have great brake lights but no tail lights. i attached there wiring diagram using a relay
LED lights do not need a relay, they draw a 10th of what your stock bulb does
the trailer light ground is white not black, this is probably where your error is.
red is "brake light/turn signal"
black is running lights (tail)
white is ground
you may have a blown fuse
your relay diagram, unless the brown wire is a ground from the rzr, you have no way to energise the relay, so your +12 volt path is directly to the brake lights. you need +12 and ground on pins 85 and 86 to turn on the relay, so pin 30 can connect to 87 NO when on and 87NC when off.