The ubiquitous Singer clamshell controller...
Unscrew the screw, then open up the clamshell, like so.
Next, vacuum out the decades worth of lint and spider remnants. You can see a carbon pile resistor (long white thing). The way this works is when the long copper strip is pressed in the center by a protrusion on the top cover (shiny spot on the copper strip), the strip bends or bows down. The first thing this does is the top strip contacts another copper strip just under it. The underside strip supplies power to the top strip. Bow the top strip down further and it tilts the left-hand side of the copper strip inward. You'll see a carbon button attached to the copper piece on the left. This button presses against the carbon pile resistor.
On my controller, there was a gap between the carbon contact and the carbon pile. When the pedal was pressed all the way, the contact point had not even started contacting the resistor, which is why my controller provided no variability. What I did was remove the contact point on the right side of the carbon pile. It is an L-shaped brass piece. I then elongated the screw hole so I could have some adjustment left to right. This next photo shows the elongated screw slot in the brass bracket.
Now you just need to close up the controller and screw the cover screw back in. I don't know how there got to be such a gap between the various parts, if it was just heavy usage over the years or if some part is missing. In any case, I now have a functioning motor controller. And it didn't cost me a cent to fix.