Someone with a jammed Amazon laminator inadvertently dislodged the switch wiring, so I took a few more pictures to help. Note: I see absolutely no reason to assume any two laminators will have the same wire colors, but the overall functions should be the same.
The top set of three switch terminals control the overall power to the laminator:
The center terminal comes from the unmarked (no ridges) wire in the line cord. The two outer terminals are connected together with a short jumper from the terminal nearest the motor, with a longer black wire to the wire nut binding other black wires.
The bottom set of terminals select the temperature:
The white wire on the center terminal goes to the wire nut holding the other white wires and a black wire (!) going to the middle of the three thermostats on the extrusion. The black and blue wires on the outer switch terminals go to the thermostats on the aluminum extrusion to the heater.
Verily, it is written: There’s nothing like a good new problem to take one’s mind off all one’s old problems.