inside each wire is a positive and a negative in their own respective insulation. you could look at that if you wanted to cut the wire. the lights wouldn't work if there was only + going to the light and no ground....
the safest/easiest way would be to do the following
1.) find out which side is + and which side is ground (take a DMM to the cigarette lighter to do this)
2.) Find a hidden area that you can stuff a few wires
3.) Solder a wire to the + side of the cigarette plug and run that wire to the battery or distro block, wrap the connection in heatshrink
4.) Solder a wire to the ground of the cigarette plug and run that wire to ground, wrap the connection in heatshrink
or you can cut and splice on the wire side of the cigarette plug