Is that a Canadian built car? Canadian built early (not sure what years) slants, used a different starter then the American counterparts. Some of the wiring was also different. @slantsixdan hopefully will chime in.
Yes, the pre-'67 Canadian-built Slant-6 cars had a different starter and control circuit. Instead of the Chrysler-built gear-reduction starter, they used a direct-drive Prestolite ("Auto-Lite" at the time) unit like the worldwide '60-'61 cars, with a solenoid like this one perched on it. The solenoid serves as the starter relay; no separate upstream relay is used (nor is it beneficial to add one). The hookup to the solenoid is the same as it would be to the starter relay on a US car: the hot wire from the "Start" position of the ignition switch goes to one of the solenoid's small terminals, and the other small terminal gets the wire from the neutral safety switch—the NSS provides a ground for the solenoid's coil when the car is in Park or Neutral. Cars with manual transmission got a different solenoid with only one small terminal and a permanent ground for its coil.