Horizontal-axis machines rotate the drum to both agitate the clothes during washing and to spin them dry.
The wig-wag is mounted atop the washing machine's transmission, where it oscillates back and forth like a railroad signaling wigwag (hence the name).
A wig-wag is a form of servomechanism; the coils are not powerful enough to engage the belt clutch themselves, but they can move their pins within the cam bar, then the mechanical oscillation of the wig-wag provides the force to push the cam bar and engage the belt clutch.
When neither solenoid is engaged, the transmission is in neutral, and only the pump is operating to drain water out of the tub.
During a normal cycle, most Whirlpool-built wig-wag equipped washers will fill, start the motor, then engage the wash solenoid.