Interface for Induction Motor
For a single phase motor to be reversible, it generally must have two windings and you must have access to connections that will allow you to reverse the connection of one winding with respect to the other winding. Switching the capacitor connection has no effect. A two pole double throw switch or relay is required. If the capacitor is switched out of the circuit when the motor is at full speed, the motor must be allowed to coast to a stop or at least to a low enough speed for the switch to reconnect the capacitor before reversing. The diagram below shows the basic connections. If there is more than one capacitor, more than one voltage connection or more than one speed, reversing is more complicated.



Re last diagram in the question:

This reversing scheme will work if the auxiliary winding is identical to the main winding. The switch will put the main winding in series with the capacitor and connect the auxiliary winding directly across the power source. Some motors may be specifically designed for this reversing scheme, but it is not the typical design for this type of motor. See diagram below.