Yeah that's very true! When I solder and shrink tape it, am I completely removing the positive and ground from the connector to solder and shrink tape it?

 

I would splice into it with solder. Use wire strippers and snip into the insulation and pull it back some to expose the wire, wrap the LED wire around it, solder, and shrink tape it. Make it like a 3-way junction since you obviously need to keep the connector on there for the bulb.

 

Raptor defently seams to know what hes talking about. But when dealing with something as dangerous to yourself and equiment as electricity. Never take someones word for it. Or trust plans. Im a automation specialist. I trouple shoot/build automated equipment and i cant tell how many times someone/plans have said this wire is this and that wire is that, and they have been wrong. Like raptor said Bust out a DMM. You can get em pretty cheap.....