What year and model?

The W210 seems to have problems with underhood grounds, some have reported engines not running and other ills so I'd start there. Look for brown wires on a stud, remove and clean the eyelets and stud. I don't know how many are under the hood but there should be at least 2 studs.

12.4 at idle is low , are you getting this number from scan tool or at the battery? If getting from a scan tool, what module is reporting the voltage?

It is possible to have low voltage through a scan tool and good voltage at the battery if a ground has high resistance.