Your car doesn't have the pushbutton controller that responds to resoldering. The parts in the picture almost never go bad. The push buttons only control vacuum on that car. The electric switch is for the compressor.
On your system the aux pump only runs when the temp is below 50 something. It is not necessary for heating unless very cold. The main heater control is through the servo.
Does the airflow from the center vents discontinue when you run the dial to full heat? If it does the system is moving (not moving is a common problem). If it moves but doesn't give heat the water valve portion is not working, try the defrost position to see if the thing can possibly heat. defrost is full heat with no decisions made.
If the servo isn't moving the amplifier is often the problem. You should be able to hear the servo working with key on engine off. have some one move the temp knob all the way cold then hot with plenty of time in between.
Bosch Master, ASE Master, L1
33 years MB technician