Take your DVOM and set it to AC and connect to a good ground and the positive side connection from the battery. Start and idle the vehicle. If you get anything more than 50mV (.05V), replace the regulator (or diode set if available & cheaper).

I just fixed a non-mb this weekend vehicle that had a 350mV 'ripple' that didn't set off the battery light and gave the same symptoms.

__________________
A.S.E Tech A1,A6,A7,A8 & MVAC 609 + EPA 608

Unless stated otherwise, any question I ask is about my greymarket 1985 380SEL.