There is quite a bit of help to find on rewiring, diagrams, detailed tutorials. A 66 might have slightly different plugs, depending on year of production, but the most common is a three pin plug. You might have knee lever controller or pedal set up, and a good place to join is Vintage Singers on groups.io. (you have to join to get acces to the files there, I can't link to them externally). A lot of technical data is stored there and expert help to be found. It's a bit easier to rewire belt driven models compared to potted.
Here's a good blog post on the subject. I need to rewire the electrics on a knee lever 99, which is about the same as a 66. It is within doable, but a bit annoying you are missing the original wiring, at least as a piont of referance.