67 switch has its overload protection inside. That is where your clicking comes from. That clicking bi-metal strip will crack in half. In other words, condition you've described is going to kill your switch. I guess that doesn't matter if its the wrong switch anyway.
If my memory serves correct, the wiper wires were moved around in the 68 bulkhead connector. This is when they routed reverse light wiring through that same connector.
My only option would be a good used 67 model wiper motor or have original repaired.
Reason being, I have to keep the next owner in mind since I know who the next owner will be ( grand daughter ).
