Wire old 240 Vinduction motor for 120 V
revised

Follow the numbers 1M to 6M on the schematic of your service manual like this one.  

Note that Line is on 4M with Neutral on 5M then the momentary switch is bypassed by 6M ( via RUN SWITCH inside motor) from Neutral and switched off by Timer or Belt detect on line to 4M.  

Keep in mind there is a separate start &amp; stop to prevent heat aging on start switch from stopping arc.



old guess

Most likely the motor uses a series heaters resistor from  240Vac 60Hz to boost starting current yet limited and then an inertial switch connects it to 120Vac 60Hz.  This may be why it is MARKED only for a dryer.  Typical induction motors use additional starter winding with Start Cap and Run cap for PF correction.  

Why did you want to go to the trouble to convert this old motor?