On singer three pin, mains lead is connected red/positive to first pin, black/negative to third pin. The foot pedal is then wired between third and center pin.
It then doesn't matter which way mains electric is connected because the pedal can work on either positive or negative side.
Only the third pin has two wires connected, one from mains supply and one to pedal.
Machine internal wiring is light between first and third pins for constant supply and motor between third and center pin for pedal control.
Old sew-tric four pins also had an earth connection.
Tony
February 2012