The M103 should have a smooth idle, and is a better engine than the M110 preceding it.

Vacuum leak may produce a fluctatuating idle speed. No real test but a matter of tracing the vacuum connectors to look for a loose connection. Spark plug cables can fracture especially if improperly plucked when disconnecting from the spark plugs.

I would not accept an answer that a M103 has an inherent rough idle. Even BMW straight sixes are smooth at idle.

Hope you sort out the problem. The M103 engine is an easier to maintain compared to the M110, and is miles more refined and economical.

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1983 w126 280SE - daily drive
1983 w123 200 - sold