I don't see the point of making rules about doing it only when stopped. Why bother at all?
You'll be subconsciously prepared to reach for the lever at every stop, because you know that these are the conditions under which someone is liable to initiate one of your "sway drills."
The load on the driver is greatly diminished at a stop as well. In a real sway situation, you'll be busy trying to keep control of the tow vehicle, mindful of any nearby obstacles and/or traffic. There's a lot more to do while moving.
Plus as grit dog stated earlier, sway events aren't sudden, unless you are not paying any attention at all.
I also agree that applying the trailer brakes when the trailer broke loose around that corner would have been detrimental.
