The link below is to a number of what I will call trailer hitch wiring files for my 2005 LR3. I do not think your 2008 RR will be much different.
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I purchased the official LR trailer wiring harness from BP Utah. I expect Atlantic British and others who can do more than spell Land Rover will have a suitable harness, factory or aftermarket. In other words, not off eBay, Amazon or the like.
Yes, sometimes there is a "switch" that has to be set in the car computer to properly activate the harness but in my case, it was not necessary.
The reason I recommend an official harness from a for real LR supplier is that our vehicles have some what I call EU protocols built into the software that are or were not common in USA vehicles at the time. The car computers are constantly checking for burned out incandescent bulbs and the number of incandescent bulbs. When it sees a greater amp load than normal, the car computer assumes a trailer is attached and make changes to the braking, transmission shift points and should disable the backup sensors.
This might be getting to be a norm in current USA trailering vehicles (pickups) but back in 2008, was not a norm except for LR.
In a perfect world, when your trailer is hooked up and uses incandescent trailer light bulbs, a little green trailer symbol lights up on the dash, something you have never seen before probably and flashes when the signal lights function.
The reason I keep saying incandescent trailer light bulbs is if the trailer lights are LED, then there can be a quick secondary flashing visible in the bulbs. This is the bulb test thing I was speaking of and the odds are, there will not be the green trailer light indicator showing on the instrument panel and hence no change to the tranny shifting etc.
This file from within the larger link explains it in better detail.
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Land Rovers are not Chevs.