My 2010 TDV8 does not have door mirror lamps which come on when you unlock the car. I have some very thin flush mount Hella LED lamps which will fit under the mirror and only require a small rectangular hole to be cut to fit them.
Is it likely that my car has the wiring for the door mirror lamps. It seems to have a lot of redundant wiring for options that it is not fitted with and I cant believe that Landrover had a different loom for vehicles fitted with door mirror lamps.

The wiring may not be inside the mirrors, it may be easier to buy some new mirros that have the puddle lights already fitted. They should be a straight swap, but as you say, the wiring loom upto that point will have the feed for the puddle lights.

I've fitted these to mine: https://tinyurl.com/yddt8r7u

The holder needed to be adapted slightly to take the panel, but they make a massive difference.

Fit a pair of RRS2 Mirrors they make quite a nice upgrade, you also get a puddle light with a logo in it.

Straight swap, just have to modify indicator wiring simple enough just connect side repeater wire to mirror wires, may have to update CCF files, I did on mine but I have surround cameras which have the puddle light integral in camera so had to tell it different.

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Click image to enlarge

Click image to enlarge

My puddle lamps have RRS outline plus words Range Rover.
I assume that's been done as after fit on dealer repair? John

RRS MY12 SDV6 HSE. Sumatra Black/Ebony & Walnut + Dynamic Pack, + Cold Climate Pack + Memory Pack, Digital TV/DVD, Premium Leather, Cornering Lights, Cooler/Fridge Box, & most Options.