The crank position sensor (L5) can definitely produce the symptoms you're describing. Fortunately, both the diagnostic test and the repair are quick and easy and inexpensive.

Here's the main diagnostic test for that L5 sensor (see FSM section 15-1250 for complete description). Engine cold. Ignition off. Multimeter set to Ohms. Unplug the L5 sensor at the EZL. Positive probe on inside of pin. Negative probe on outer part of pin. Spec is 680 -1200 Ohms. If no, rplc L5 sensor.

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1988 California version 260E (W124)
Anthracite Grey/Palomino
Owned since new and still going strong and smooth
MBCA member

Past Mercedes-Benz:
1986 190E Baby Benz
1967 230 Inherited from mom when she downsized
1959 220S Introduced me to the joys of keepin' 'em goin'

There are only 10 kinds of people in the world--those who understand binary and those who don't