Hi,
If that is the HVAC controller above the radio, the brown wires provide ground. So, that certainly would cause the system not to work.
As far as soldering, it can be done in a traditional manner. The only issue is if the gold which is placed to a different metal comes loose or separated, you will lose connection.
Looking at the pic, it is difficult for me to identify what has broken. Can you explain? Also, I attached the wiring schematic for the HVAC system specific to this vehicle. I wanted to attach it so you had it as a reference.
Let me know.
Joe
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Saturday, May 29th, 2021 AT 10:39 PM