Shouldn’t I be able to use my cigarette ... where nothing you plug into a 12v accessory socket works, the first thing you'll want to do is check for obstructions inside the socket.

CIGARETTE LIGHTER SPLITTER ADAPTER - Splits 1 car cigarette lighter port to 2 DC ports, 1 cigarette lighter male plug to 2 female ... the car's power port. Two 12V/24V cigarette lighter sockets ...