What do you want to achieve and how do your current lights behave?
My assumption is that they are just running from the OE wiring given you point out the OE switch? So I would expect them to turn off after 20 mins or possibly 60 mins?
If you just want to turn them off during that time window then you can simply find the wiring feed and interrupt it with a switch.
If you want to be able to turn them on after that timeout then that's a bit more complex as you would need to provide an alternative 12v source (and risk battery drain)
Normal lighting appears to have 3 lines:
A switched ground wire that connects to ground when a door is opened.
A 12v feed controlled by the BCM that times out (to save battery)
A permanent ground wire (this may not be present if the OE wiring is for cargo type use rather than passenger)
Under normal use the lights use the switched ground and timed 12v; when the doors open the switches ground connects and lights come on. If you leave the door open after 20/60 minutes the BCM turns the 12v off to save power and they go out.
With passenger style lights you can use a switch to change the ground from the switched ground to the permanent ground. This will keep the lights on regardless of the door state, but as the use the timed 12v they will still eventually be shut down by the BCM after 20/60 mins.
The console switch is essentially picking one of three ground options:
Unconnected - lights will never come on
Switched ground - lights will come on with doors until timeout
Permanent ground - lights will stay on until timeout
You look like a 6.1 so be aware the switched ground isn't an old style on-off. It's electronic doing PWM dimming so that lights fade out and also they don't go off straight away on door close but a few seconds later. That's important if you want to think about using a relay triggered by that circuit.
Lots of info over on this thread:
LED rear interior lights - How i done it. so a few have asked, so i though i would just list it here as a post so i could refer back to it in the future. The lights were purchased from The T6F shop over here > We were planning to do the carpeting at around the same time, but for the purpose...
www.t6forum.com