If your 1960
is like mine, and all the other 1960's that I have seen, The unbilical (the part that plugs into your tow vehicle) is simply a 3 foot section of wires with a plug on both ends. It would be best to replace the whole thing. If you pull the plug on the trailer and inspect the trailer's belly pan wiring you will find that all of the wires to the lights are red. The only difference is the number of knots tied into each wire. Many years ago I knew what # of knots went with each circuit. I cannot find that info right now. If you really want it you will need to wait a few days before I can dig into the trailer. What the inspector is conserned about is the condition of the wires on the umbilical (from plug to plug). Like I said, it's best to replace them. You can purchase a length of bargman wire (all color coded and wrapped together for some unreasonable amount of money from an RV place, or you can purchase your own wire and do it yourself. There are wiring diagrams for the plugs online. One such is at: 7-way - 7 pole RV Travel Trailer Connector Wiring Color Code
When your trailer was built there was no standard...or at best Airstream ignored it. Wire it to the current standard...as per the website mentioned above. Take your time, you may make a mistake or two, but it is not rocket science.