I looked up the klima for a 300E to see if it was also used by 4cyls. By the number it doesn't. The relay watches that the speed number ratio stays the same no matter the numbers. I don't know if it also has expectations.

If it expects a certain ratio between rpm of the compressor and the engine (which would change with engine cyls because the speed signal is actually just a punch of pulses divided by 4 or 6 sorta) then the system would always shut off after starting up. If it has ever worked with that relay then the amount of cylinders don't matter. It still might be bad, but whether the part is wrong is an either or situation not a maybe all of a sudden.

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Steve Brotherton
Continental Imports
Gainesville FL
Bosch Master, ASE Master, L1
33 years MB technician