Automotive wiring can become damaged and will need to be repaired over the lifetime of a vehicle. You can repair wiring in multiple ways; however, automotive industry standards dictate the proper way to repair damaged wire is to solder the broken pieces together to create a strong bond that is equal to the strength of new wiring.
Put on the safety glasses. Disconnect the positive and negative battery cables from the vehicle's battery using the socket and ratchet.
Place a piece of heat-shrink tubing over either side of the broken wire and slide as far away from the break as possible.
Trim back the remaining protective coating with the wire trimmers and provide about an inch of bare wire on each end of the break, then overlap and twist the wire together, creating a strong connection.
Heat up the soldering iron and solder over the twisted wire. When done correctly the heat will cause the solder to wick into the wiring, creating a strong joint. Allow to cool and provide a gentle tug to the wire to ensure a good solder.
Slide the heat-shrink tubing up and over the bare wire joint and use the heat gun to shrink the tubing, effectively creating an air-tight seal.