How to wire in a motor controller

I have a 50s vintage Morse zig zag sewing machine in the basement that has the two plugs coming off the machine, one for the motor and one for the light. Here's what the plugs look like, along with the $2 motor control I picked up at Goodwill to connect up to the machine:

Fixing an old Singer 'carbon pile' foot control

Tonight I was working on a Singer 758 sewing machine. This machine looks to have been used very heavily. I adjusted and oiled it, then noticed the foot control was one of those that is either on or off, no variable speed in between. The machine has two speeds but having variable speed control would still be nice to have, so I ventured into the depths of the foot control.

The ubiquitous Singer clamshell controller...