All the wires you need are already there at the back of the car, on your passenger side.
The towing electrics hook-up connector contains a Reverse Lights feed and an Auxiliary live.
The Reverse Lights feed is Green with a Brown trace (GN)
The Auxiliary live is Purple with a Brown trace (PN) and is fed from Fuse 9 (25 Amps) in the engine compartment fuse box.
Use the GN wire to trigger a relay to switch the PN wire, mount the relay at the back of the car behind the RH (passenger) side trim.
You can splice into the wires behind the trim, before they go through the grommet to the towing hook-up -
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The first two pictures show the location of the towing hook-up and the wire colours that go to each pin.
The last picture shows the wiring loom behind the RH side trim (with the trim removed), it's annotated 'drivers side' because it's on a RHD vehicle and 'header' refers to the Grey/White earth header bolted to the body (a good place to earth your work lamp and it's relay)
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