Wires only break themselves for one of these reasons: overcurrent (they melt), pull action or repeated bending action. I bet your wire is broken at the steering junction, where the frame loom goes into the headlight shell. If it is broken, pulling the cable will extend it, meaning that the copper is broken and only the plastic insulator is there. Breake it, connect both sides together and you are good to go.
Raul
P.S. Don't forget to put duct tape at the end...;-)