the plug feeding the cigarette lighter is hot (has 12 volts) all the time, be careful in connecting them you don't short them out, it may be recommendable to disconnect the battery before messing with them.
BTW I believe you will find that US appliance plugs won't fit or won't fit the MB socket well, the sizes are different for some reason.
I plan on installing a remote cigarette lighter socket somewhere on my car. I haven't decided where to mount it yet.

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'95 E320 Wagon my favorite road car. '99 E300D wolf in sheeps body, '87 300D Sportline suspension, '79 300TD w/ 617.952 engine at 367,750 and counting!