The EDS system does put out blink codes from the plug by the battery. The test system is similar to the gas cars of the era and can use the same blink code reader. The later 603's system is above my pay grade for troubleshooting. The earlier cars had a trim wheel by the brake booster to set the idle speed. If the 350 has one, try setting it to a higher number like 5 or 6 and it should boost the idle speed. It's always possible that the solenoid or wiring is bad too. If all else fails, you can set the idle speed manually with the adjustment bolt on the back of the IP.

The EDS system controls mainly EGR functions and tach signal to the devices that use it. Later cars used the EDS system to control boost via a vacuum operated wastegate and the ARV on the turbo if present.

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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]