There is one other function that the Klima relay performs that is not taken care of by the solution above: There is a delay engaging the compressor clutch until the engine is running at an RPM above crank speed.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]