Get a wire thats the same size as the one you cut, should be a 16 gauge if I am thinking about the right one. Then open the harness so you have more room to work on it. To open the harness, look on the side you should see little ears that keep it closed, push down on them or bend the plastic keeping them in up, and it should open up. Make sure not to break anything. Get a small piece of shrink heat wrap from Home Depot or Radio, and slide is onto the stock wire. Then tin the wires in the places where you are going to solder them, so they will stick together. Then touch the wires together so they stick. Make sure to keep your hands nice and steady. Once they are together, slide the shrink heat wrap on top on exposed areas of the wire, and squeeze onto the wires. Then use a heat gun, or a hair dryer, or a paint peeler, etc, and expose it to the wrap all around; just some quick exposer, NOT TOO LONG. Then if you want you can test its impedency, in order to make sure its getting a signal and not getting distorted. If everything checks out then you are good to go.