Cruise amp is the most likely candidate. I had exactly the same problem on our 380SL.

Simply disconnect the electrical connector to the cruise actuator in the engine bay until you get around to diagnosing the issue. There are many many excellent posts on the cruise system in here if you use the search feature.

Do NOT expect a cruise amp pulled from a picknpull to be any better than the one you have now. It will have flaws too - perhaps different. A reman, guaranteed unit is the way to go.