I'm not sure of the wire route on the UK built cars, however, the Aust built cars had a pair or wires that ran from the switch, along the steady rod of the shifter, then clipped to the LH and front side of the front subframe, where it ran up with the rest of the engine bay harness.
One of these wires got a feed from the Fuse Box and the other ran around the firewall, disappearing up the LH front pillar, along the internal gutter (under the roof lining) appearing back out near the fuel tank and then on to the rear lights.
The way the wires got to the switch wasn't one of our best bits of work,,,,
I worked on an Aussi Clubman were the reverse lights were built into the rear indicators using dual filament bulbs. The bulbs were rated 21/21watt which we connot get in Europe, can they be got is Oz?
We can get them easily. If you need some pm me.
Thanks. the mini has changed hands since and is for sale again . If I remember right I think a boot mounted light was fitted but I will let the owner know the blubs are still available. Personally I would go back to the original as it is such a rare setup in Europe.