Unlike the W113s, you don't have to disassemble the dash to work on the W111 heater controls. Just take off the lower cardboard panel and radio, and you should have decent access. The levers are replaced without removing anything. They are just clippped in.
If the lever arm is actually moving the controls inside the dash, sounds like a cable clamp is loose. For the heat control, there is one clamp on the control mechanism and the other clamp is on the heater valve just above the trans hump. All easy enough to get to. I just went through all of mine this spring.
You can also use a cable luber to lube all of the cables for good operation. See motorcylce parts shops for that.
I hope this helps.