You've got a poor connection between the battery and either ground on the negative post, or between the battery and the positive circuit on the plus post. Take your digital voltmeter and while it is failing measure between the center of the negative terminal and the engine head for voltage. If you see 12v there it's the ground circuit. Then measure between the center of the positive terminal and the alternator's 12v output terminal. If you have voltage there you have a poor connection in that circuit.
It has been my experience that 99.6 % of these problems are right at the battery posts. MAKE SURE you have cleaned those well, and have them tightened well. They MUST be shiny and clean. They can be physically tight and look fine to all appearances but still be failing. You have to remove them to check them! Also, wiggle the wire attached to the starter terminal, and wiggle the wire going from the negative post to it's grounding point. You should be able to find this problem in minutes with a meter.

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Richard Wooldridge
'01 ML320
'82 300D 4.3L V6/T700R4 conversion
'82 380SL, '86 560SL engine/trans. installed
'79 450SL, digital servo update
'75 280C