I had a hard time seeing, but it did look like one of the, what I call, pins in the machine had gotten pushed in. Unfortunately, I can't help. I am fairly certain there are only three pins, but as bkay wrote "However, it's not unusual for a plug not to use all the slots." In other words, the plug (that goes into the machine) that the wires go to the wall outlet and foot controller has four holes. The machine only has three pins (pegs). As bkay mentioned tandtrepair is knowledgeable about the slant shank Singer machines. I noticed that he does have a service manual for the 640 series, but unsure if it would include the wiring schematic.
https://store.tandtrepair.com/tosew600se.html There is a button at the top of that page "email us" that you could probably use to ask.
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Janey - Neat people never make the exciting discoveries I do.
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