Rear brake lights out

not sure

Depend in the year of the vehicle the the rear brake lights could be pulse width modulated. A lot of times the vehicle need to be reprogrammed to lower the intensity of the bulbs. This can cause both lights to burn out at the same time. It can also cause the actual light assembly to start to melt. If it is an older vehicle resistors have to be wire in series with lights to prevent them from burning out. I had to do this with my 05 c class for the license plate lamp lights. Otherwise it is very common for bulbs to fail at the same time or close to it. I would first check the bulbs and fuses and go from there. Check for discoloration or deformity in your light assemblies as well. If that is present you know more repair is needed.

The housing metal where the socket makes contact is burnt or it has an indentation from the high heat of the current, I cleaned that, soldered over to build it up flat again and it works now because it makes good contact now. Saved $400 that the dealer wanted to charge to change the whole housing.

Now after soldered to build up the indentation created from the current high heat

It works like a charm now

I had a similar issue on my 2011 ML350. My issue was the bulb socket was indented so I had to build up the contact . Light is now working.