That's another thing - the video shows it very well. After all, why a stepper motor? It seems to me that a simple DC motor will do the job. You will need a motor (maybe with gear), a 3-position switch and 2 limit switches. If you want to do something more complex such as oscillating left / right without stopping then it might be easier to add an Arduino (although Arduino is not necessary for oscillation). From where will you get power supply for the motor? Does the machine have a battery, for example?