Brake lights wiring question
 

Previous owner upgraded tail light and it looks like connectors had to be adjusted.
https://i.ibb.co/mJ3BVwr/20210214-223233.jpg

This is the right side, and everything works fine
https://i.ibb.co/xjcH2Mt/20210214-223324.jpg

Unlike the left side. On the left side the stop lights don't work. So what he did is connected the wire from the right connector across to the left .
https://i.ibb.co/fSg95T4/20210214-223517.jpg

You can see the right connector. Brown is obviously ground, and one to the left of ground is the power. It has an extra wire coming out of it.
I need to connect it to the left tail light connector.
It has 12 volts with the brake applied.
The left connector does not provide 12 volts, so the stop light doesn't work independently. I tried checking a few extra wires (probably leftovers from original taillights) for voltage but no luck.
Another confusing thing is that left and right connector wires are totally different color. I wanted to copy wire color from the right side and make the same connections.
I wonder if it's possible to get the stop light working again without running a wire across the from right to left

You are working in a pretty big can of worms there! First thing you need is a wiring schematic to follow, and then very likely a scan tool to diagnose/code the LCM (light control module) Are the replacement lights LEDs ?

What age is your X5?

The car is 01/2002 (last 7 VIN LP39173)

The bulbs are not LED
https://i.ibb.co/zm8Q436/20210215-072404.jpg

Seems like it only has 5 wires that are going toward that connector. 2 are disconnected, but they don't have power anyhow.
The one with the yellow clamp is the wire coming from the right side to provide power
https://i.ibb.co/KD229vN/20210215-073411.jpg

I did remove a LCM from another X5 the other day.
I haven't totally figured out how to test the LCM.
Is one of the 2 wires that are just cut off is supposed to provide 12 volts with breaks applied?
I guess I can't just plug in another LCM without reprogramming it first?

Tail light (US 9/2001-3/2002)

Left X319
*Side light, grey/purple, pin 3
*Direction indicator, blue/green, pin 4
*Brake light, black brown, pin 5
*Brake light (force dependent), black/green, pin 2
*Ground, brown, pin 1

Right X318
*Side light, grey/white, pin 4
*Direction indicator, blue/brown, pin 3
*Brake light, black/blue, pin 2
*Brake light (force dependent), black/white, pin 5
*Ground, brown, pin 6

Yes I've seen this.
I was wondering how to test.
I can see that left and right break pins are on separate connectors of the LCM.
So I measured voltage on the back of pin 14 on connector X38, when connected to the LCM.
Pin 14 is responsible for the rear right brake light. I got 12 volts.
https://i.ibb.co/k1rW4jP/Screenshot-...857-Chrome.jpg https://i.ibb.co/xmt62q7/Screenshot-...225-Chrome.jpg https://i.ibb.co/fN5WCKR/Screenshot-...259-Chrome.jpg

Now I went to connector X12 on the LCM. Pin 9 is responsible.for the rear left brake light.
I measured the voltage on pin 15, which is the power supply, it has 12 volts. Then I measured voltage on the back of the connector, pin 9, and got no voltage.
I did all tests with the connectors plugged in and brake pedal applied.
Looks like LCM is not supplying voltage for the wire on pin 9.
Does this condemn the LCM?
https://i.ibb.co/R2VGLq5/20210215-093816.jpg https://i.ibb.co/Sx4Qmd8/20210215-093823.jpg https://i.ibb.co/QHkwRMf/20210215-093852.jpg

Yellow is the old module and white is the one from scrap yard.
https://i.ibb.co/cLKZhx3/20210215-095143.jpg https://i.ibb.co/5n5FjtH/20210215-100541.jpg
I'm wondering if I need some software for coding or if I can try plug and play?

I think I found the problem in the module
https://i.ibb.co/Lt4bddv/20210215-102439.jpg https://i.ibb.co/k6Fc2X9/20210215-102434.jpg https://i.ibb.co/BNB4cDQ/20210215-102427.jpg

There could be a short to ground in the circuit that isn't working so you shouldn't condemn or replace the LCM just yet.

The LCM holds the mileage along with the cluster. If they do no have the same mileage and VIN, you will get a tamper dot on your cluster next to the mileage. It will still work fine but may not pass annual state inspections.

To recode the VIN and mileage of the used LCM, you will need PA Soft 1.4 and a laptop running Win XP or later.