You're going to build a homemade lathe and you can't figure out how to do this with a multimeter or otherwise? Good luck sir, be safe!

There is a site on the net which gives repair advice for large appliances and shows details of parts in blowups. I've forgotten the address but you can find it by googling: appliance repair

This might be difficult to do with a multimeter, at least for anyone not well versed in all the possible motor designs. Measuring inductance and capacitance may be needed, and one then still has to infer a lot.

This motor might be designed to run at different speeds using different wires, or run two phase or three phase from an electronic motor controller. Or, two wires might be for a speed sensor. This would be a good project for a sophomore EE lab project.

If the motor has identification of who actually manufactured it, then a specification might be found. Then again, an appliance repairman might happen to know how it is used.

kas

might be easier and quicker to just get the wiring diagram from MAytag. They have one , and it will show the what those wires are connected to.

What country are you in, or more to the point, what country is listed on the placard as the intended installation site?