I think there might be two different things being described here.
1. A kid who is constantly moving and moves even more when they are excited. This kid is moving and still engaged with the people and activities around them.
2. A kid who uses a repetitive movement (like pacing) to get lost in their own thoughts. While doing this, they are not interacting with anyone.
What my DS15 does is #2, and he doesn't do #1. When he is busy twirling, he doesn't want anyone to interrupt him. Oddly when I was filling out all the "questionnaires" for my son's testing this past month. I didn't see this asked about anywhere, not one question even alluded to this kind of behavior. Even in the ASD questionnaire.
