Fantastic fan switch part #

Fulltimers your very helpful observation that the two tabs on the back are a switch got me busy with the meter to see what is happening. Indeed the knob for the pot starts with a "click" and that is turning power on to the pot. The "wiper", on a good switch, does have a voltage drop from nearly 4 volts when fan is zero speed, slowly dropping to 0 volts as the fan increases to max speed.
On my problem pot, when it is switched on, the voltage immediately drops to 0 volts and max fan speed is noted.
I did not find a pot that also had this switch so will add a little toggle switch along with a replacement 500k pot, all on order.
Thanks to all who offered help!

If yours has the 3 terminals along the side and 2 on the back, the 3 are the pot and the 2 are a switch.

do you see the right one here? Fan-Tastic Vent Exploded Parts Views
there are a bunch of companies that sell parts for them.

Might not be the potentiometer. It might well be the control board inside the fan. On mine, the pot can be used for either speed or temperature and the actual control of the motor is done by a circuit board inside the fan housing.

I had not heard of Digikey, thanks for the suggestion. There is a 4 digit number on the pot (0421). Plugging that in at Digikey under "Potentiometers" suggests the pot is 500k but otherwise does not resemble my problem pot which has two tabs sticking directly off THE BACK. Everything seen so far has just three tabs across the edge (which the problem pot also has).
I will be looking around on ebay to see if something resembles it. Thanks again.

Get the part number off the pot and go to DigiKey and buy one.