Can someone with knowledge of wiring schematics look at a wiring schematic and determine what each wire does in the motor?
Yes... possibly, but not without your help. What you are showing is a wire diagram, not a schematic. I can only understand what should happen if I turn it into a schematic- that is what tells an electrical engineer how it works. Fortunately I am one. A wire diagram shows people where the wires connect- that's a much different thing. I've been trying to understand the purpose of the "coordination switch". Happily the wire diagram shows what is happening schematically inside the motor, but it doesn't for the dash switch. That shouldn't be a problem- given enough information I can deduce how it should work. The coordination switch may show what happens, but its a little difficult to make it out. So, if you want to proceed, here are my first set of questions;
1. When it was working properly, describe how the foot switch worked- because I can envision a couple of possibilities. If you don't know, do you happen to have an owners manual that describes what is supposed to happen? Maybe someone on here could help?
2. Can you use an ohmmeter? If you can't you are going to need to learn, but its not difficult. This will take a fair amount of back and forth, but we'll get there. We both need to be patient. I often assume people know more than they do, so I may ask what seem to be stupid questions.
3. Please take my advice and STOP aimlessly plugging wires in when you aren't sure where they go, or you could easily cause a short, melt insulation off wires, or blow up some or all of the components in the circuit. Sorry, but it drives me crazy when people do that. Perhaps you already have damaged components, but we'll figure that out once I understand how the circuit was designed to operate.
FYI, the wiper circuit on my 69 is one of my favorite on the car, because there is some real science going on there. I won't get into it now, but I'll explain once I understand specifically how your 67 works. I'm sure the 69 is a derivative of the 67.