The original wiring in my two '82 300Ds connects the radio to the cigarette lighter connection through a short harness. I would connect yours there. It shouldn't run the battery down that way.
Assuming your after-market radio has a clock and internal station memory, it will also need a connection that is always hot. The fuse block can be a bear to get to, so I would connect that wire either directly to the positive terminal on the battery or to the hot side of the rear seat light switch. The rear seat light switch on mine is on the left at the top of the center console.

Hope that helps...

Wes Bender