"Anonymous Usually the word Swing is reserved for a body that is swinging past. A meterite swung past the earth."
And that is what a dancer does - moves on a path through space that is curved in the vertical plane due in large part to the effect of the earth's gravity.
The existence of a partner is irrelevant to that. It only comes in for determining how big the swing should be - larger for the person on the outside but smaller for the person on the inside.
"Which leads me to beleive that the word swing in dancing is for the person on the outside of the turn and not the person on the inside."
I hope that you are not under the mistaken impression that you swing around your partner, because you have in the past recognized that the movement are generally straight lines across the floor during step 1, and that means that the only direction in which the swing can curve at that time is in the vertical one.
"Let the person on the inside of the Swing follow the instigator of the Swing, which if body contact is maintained must be delayed NFR and will be a smaller action."
Smaller, yes, and the foot action is NFR but as you would see with Marcus and Karen on that video is it not delayed at all, but occurs as a continuous movement at the same time the person on the outside is moving. There simply is no pause on the inside with real dancers of that level. If it were delayed, then the person on the outside would have to curve their path to maintain a constant distance from the temporarily non-moving inside partner.
"Just like the Gyroscope whose action is centrifugal."
No, not at all like a gyrscope, because the path across the floor is NOT CURVED.
"The centre does not Swing."
On the contrary, in many situations such as downswings or the upswing into the double reverse it effectively the only thing that swings. The whole body goes along for the ride, but does not develop an incline, so you can reduce it to a simpler model of a point mass at the center of mass.
"If both travell at the same time at the same speed covering the same distance. In theory the man will never get around to where he should be."
Which is why, as I have been saying all along, you must travel at the same time, but NOT at the same speed and NOT cover the same distance.