Two Speed Timer for 110V Motor

Hello all, I have a Century B2981 pump motor and I'm looking to hook up a two speed timer. I have 120V 20A going to the motor from a single breaker. It seems like if I had 220V I would be ok because I could use a T106R timer, but I can't find the 110V equivalent and the timer motor in the T106R timer appears to need 220V to function.

Does anyone have any ideas here on what I could use for a 110V motor timer?

Thanks in advance!