My left rear fog light doesn't work. I know for sure that the bulb and the socket (see attahced images) work. I switched between left and rigth lights to check.
How do I check the wiring? Can I first of all check the voltage just by sticking the multimeter inside the socket? If yes and it shows 0 voltage, what should I check next?

 

Check newtis.info for wiring diagrams.

 

The only relevant thing that I found is this one. Can you explain please what exactly should I check?

 

You can check few things:
1-do you have ground? Connect the tester to the brown wire on one end and the other end to the positive terminal of the battery. If it lights, then your ground wire is fine.
2- do you have signal? turn the fog lights on, connect tester to the other wire in the plug and other end to ground. If it lights, the ground wire is not good.

 

Just to be clear, the brown wire is the ground and black is voltage? How can I reach the (+) of battery from the back of the car, with a very long wire or there is a more easy way? Do I need to put a resistor in beween? Where is this brown in the images I posted?

 

yes

you can use a long wire. we dont want to use the signal wire off of the other fog light. we want a clean path.

no need for a resistor. you light tester should be fine. it is deigned for that.
remove the table around the two wires to see the colors.

 

You need to unwrap some of the insulation tape to see the color of the wires inside. The other way is that in the wiring diagram, ground (brown) is on pin 2 of the bulb socket connector. There should be tiny numbers embossed in the connector plastic identifying the pins (only pin 1 might be marked; the other would be pin 2). You should see continuity between the ground of the left and right side bulb sockets.

 

I don't have a light tester. I have a regular multimeter like this one . Can I just connect the red prob from multimeter to (+) of the battery and the black prob to the brown wire and check if I have enough valtage? If I can, how much voltage I should see?

 

you can do that....around 12 to 13v. depending on the battery voltage.

 

Are you talking about this connector? If yes, can I first of all just insert the niddle probs from multimeter to pin (1) and (2) to check the voltage?

Can you ellaborate on this?

 

I'll try to do this. Can I also just check the voltage between the pins (1) and (2) in the connector as shown here?

 

Continuity test: based on the multimeter image you linked, turn the **** to the red position near the bottom. Touch the two test leads together — you should hear a beep. You should also hear a beep if you touch the test leads to the grounds of the left and right bulb socket. That would indicate a good ground connection.

 

you could. i thought a good bulb was installed and wasnt lighting. that means no voltage will be across the pins.

 

I had this problem. MINI wanted to replace a module ($$). I said no.
I cleaned the contacts on both the bulb and the socket. contact cleaner and abrasive too. It didn't come back on immediately but it did after a moment. The computer had to think about it.
Dern fangled lighting still follows same old rules of electronics, bulb sockets still corrode, but now you have some software looking for bulb present , bulb shot, etc before she decides she will power up the bulb.