Not my sketch but this is correct. I changed both my Carlton and my no-name model this way, just remember the motor has to slow down significantly for the start windings to take over and spin it the way you want. Don't worry if you don't have the light, just ignore that line.
An alternative is to spin the wheel whichever direction you want it to go, then power it on. It may be necessary to use a drill for example to spin it fast enough to overcome the start windings.
I cannot tell anything from that photo. In essence, the start and run windings are joined together and connected to the hot and neutral lines. You need to locate and separate the start winding from the run windings and connect them through the DPDT switch in order to change the rotation.