This is a pretty late reply to this, but in answer to where did I run the wire...
If you pull the light above the bed down, you'll find that the wiring is between two layers of thin plywood- the bottom of the cabinet, inside, and the bottom of the cabinet, outside. I drilled a small hole up through the existing hole for the light wires, and tapped into those 12 wires for power and ground. Since I put the speakers in the ends of the cabinet, I just ran the wiring along the bottom of the front of the cabinet and used some Gorilla tape to "hide" them.
I actually ended up just leaving the antennae in the cabinet, inside the camper. We've been able to get stations everywhere we have been.
I was trying to figure out how to post pictures, but I don't have that sorted out yet.