I had that happen once, a very long time ago. I remember trying to duplicate it on several occasions, and nearly had it a couple of times. A few variables have to mesh to make it possible. Fascinating how the rocking motion and the oscillations in the line seem to strengthen each other. One thing I remember is that the tail has to be just a little bit less than what the kite can possibly lift, and the rocking motion of the kite can be amplified by making the distal end of the tail heavier than the rest of it, for instance, using a rock or other object to add weight to the existing tail. I spent a whole summer trying, but never got it to work as well as the time it happened initially.
The weight of the tail, wind speed, length of the tail, weight of the line, length of the line, area of the sail, how high or low the attachment point on the bridle, and even the bow in the frame that the wind creates all have to be in exact proportion to each other. Absolutely mesmerizing when it happens.