Interaction of vision and movement via a mirror

I have noticed a striking effect that vision can have on movement: when a person makes circular motions with both hands, clockwise with the left hand, counterclockwise with the right hand, while watching the reflection of one hand in a parasagitally placed mirror, if one arm makes a vertical excursion, the other arm tends to make the same vertical excursion, but not typically if the excursing arm is viewed in plain vision. This observation may help in understanding how visual feedback via a mirror may be beneficial for rehabilitation of some patients with movement deficits secondary to certain neurologic conditions, and illustrates that the traditional division of neural processes into sensory input and motor output is somewhat arbitrary.