A/M has 2, Bronze and Silver. Its in F/T and W. Foot closure in Bronze.. Open in Silver
What you describe as Arthur Murray actually sounds more like Fred Astaire to me. Fred Astaire adheres more strictly to the NDCA concept of foot closures in bronze, foot passing in silver. They have several versions of Twinkles, all of which keep the feet closing on the 3rd step, right through the last step in the bronze Waltz & Foxtrot syllabus. They don't introduce foot passing actions until silver.
Arthur Murray, in contrast, traditionally didn't have any foot closing Twinkles. In their most recent syllabus overhaul (about 5-6 years ago, I think), they added one single foot closing Twinkle to their intermediate bronze Waltz syllabus. However, once a student graduates to full bronze (figures 6 through 10), they ditch the foot closing, and move right on to foot passing Twinkles, of which there are several. It's a shame, because not enough time is spent on foot closing to make a lasting impression, and the student followers in particular suffer, because they typically have difficulty following any type of foot closing Twinkle, even when properly lead.
I haven't seen the DVIDA Twinkle in print, but I can't imagine it's very different from the others. Everybody has slightly different ways of describing the technique, but ultimately the fundamental Twinkle is danced the same.
A Twinkle is a difficult word to define because so many types of figures have been labeled as such. One might be inclined to say that it's a figure that transitions from closed to promenade position and back, but that would exclude all "Passing" or counter-promenade Twinkles, among others. In fact, if you go by the Fred Astaire definition, you can't include dance position at all; They attach the "Twinkle" label to figures that stay closed (e.g. "Progressive Twinkles", which we call Closed Changes O.P., or Passing Changes in silver), Shadow Twinkles, etc. They even have a figure called Twinkles in Cha Cha.
So to be as inclusive as is reasonably possible, the best definition I've come up with is this: A Twinkle is a movement consisting of 3 or 6 steps, usually involving a deviation of direction, and sometimes a change of position, such as closed to promenade.
Regards,
Jonathan