I'll wind up this little mini-series of one-step posts with an easy variation from Vernon and Irene Castle's manual, Modern Dancing, (New York, 1914). The zig zag is very similar to the snake dip described by Philadelphia dancing master Albert Newman (discussed by me here). The oscillating from right Yale position (the two dancers' right sides together) to left Yale position (left sides together) with the lady backing up while the gentleman moves forward is the same, with the differences found only in the starting foot and the placement of the dip. I have no doubt that these are simply regional variations of the same step, but they do have a slightly different effect when danced.
While the snake dip begins with the gentleman stepping to the left (right Yale position) with his left foot, the zig zag begins a beat later. After one walking step forward on the left foot (lady backing on the right), the gentleman crosses his right foot in front of the left to step out to right Yale position, taking three steps in that position (right-left-right) before crossing his left foot in front of the right to shift to left Yale position and take three steps (left-right-left) thus. The lady is dancing opposite, crossing her left foot behind her right to start the move and continuing on th opposite foot from the gentleman, always crossing behind.
The zig zag may be continued indefinitely, exited most easily after any trio of left Yale position steps by the gentleman simply not crossing his right foot over, instead stepping straight forward toward the lady and resuming backing her up for as many steps as needed to round out the musical phrase.
The Castles suggest ornamenting the step with a slight dip:
To make it more effective, the dancers can bend on the first step. That is when the man crosses the right over the left and when he crosses the left over the right.
This bend is actually on the same foot as in Newman's snake dip -- he places the dip on the second step of every three-step diagonal, which is effectively a crossing step.