I've only owned my 560 SL since before Xmas 2008. It has started instantly every time I've turned the key. It fires and runs at 650rpm. However, it seems to me that the engine speed should be higher, even if for the briefest moment. Having said that, I should also mention that I have never started it when the ambient temperature was under 50 degrees.
Am I looking for trouble that doesn’t exist? Or should I be looking to replace some malfunctioning part?

I gotta tell ya, this is the first 'low idle' post I've ever read, almost everyone has complained about high idle on the 116/117 engines. There's little to check on the 560SL outside of the IACV, the control box, senders to the control box, and vacuum leaks, and it's a very frustrating exercise. Count your blessings.

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1986 560SL
2002 Toyota Camry
1993 Lexus