It has been my experience that when someone describes a "front end wobble" it will happen when going over 100mph even in a straight line. The front end wants to wiggle and some gyrate to tank slappers. I've heard this has something to do with the steering head design and alignment with the rest of the bike. Something in relation to a minute offset in the triple clamp/steering neck design in relation to the rest of the bike. Don't quote me, but this is one of the replies I've heard in relation to front end wobble.
The wobble you are describing and seeking clarity seems exactly what happens when the rear end begins to oscillate. The harder you push in a turn, the worse it may become is my experience. Even moreso with some variations in the transition of the road itself in a turn.....ie.....hills/bumps in the road through a turn......and the wobble then becomes more evident.
This brace and from what others report from the other devices are the answer to keeping the rearend from dancing around keeping the scoot properly aligned, without unwanted flex, for a much more fluid handling of the bike in aggressive riding conditions. The overall benefit also contributes to low handling stability as well.
My $.02 anyways.