The problem here is the motor's wiring diagram would only show a permanent connection, with the rotation direction set.
In the case of an application where one needs to be able to reverse rotation using an external switch, the starting winding connections need to be removed from the motor's terminal strip, and routed thru the double-throw reversing switch on the lift controls.
This is more complicated than the motor's nameplate would be able to deal with, and requires some knowledge of wiring and circuitry to connect right the first time....