Simple wiring advice.

I want to install a strip of LED lights that I bought from Jaycar into the kitchen side of my traytop camper to replace a pretty useless fluoro that we've been using.

I thought that I would put a switch between the light strip and the power source. As the power source, I was simply going to tap into the wiring that feeds a permanent, not very bright, but useful in a hurry, bulb type light that is attached to the wall of the camper's kitchen.

Pretty simple I thought, forgetting my fairly low tech electrical understanding. When I checked out the wiring into the permanent light I discovered that it only had one wire going into it. This wire is brown, so I'm assuming that it's +ve. It seems that the circuit is completed by a short wire, inside the light cover, that's attached, at one end, to the steel wall of the camper with a rivet, and to the light switch, at the other end.

Now, the brown wire, which I assume to be +ve, is connected to another brown wire via a standard connector/junction fitting. This connector/junction, also has a white wire going into it, which I assume connects to the steel of the camper somewhere to provide the circuit.

Can I assume that this wire is the -ve and that I could wire my -ve wire from the LED into it, or would I be better off running a new lot of wiring that I know to be +ve and -ve.

I do have a plan B which is to connect the LED strip up to a cigarette lighter plug and use the plughole fitting in the camper. I don't want to do this if possible as the plughole is useful, and the solution isn't that neat.

The LED strip, btw, should be a cracker when I get it up and going. Very unobtrusive, and very bright.

Many thanks,

Jeff