Is fidgeting always a sign of agitation?

My son as a boy would bounce his knee when he was doing his homework. A teacher would tell him to send a message to his knee to stop bouncing. He would and it would stop for the moment.
Some folks tap a pencil or doodle. Some drum their fingers. I’ve never associated it with agitation but I’ve never noticed anyone make large swirls or movements as you describe. I always thought my son wanted to move about, not be confined to sitting at the table but the gentle reminder would make him stop. More impatience than agitation I’d say.
The web mentions repetitive movement of objects having to do with autism in adults.
I had an aunt who during her last days would make a large movement that we identified with quilting. She would go through the motions of pulling an imaginary needle and thread through a quilt and pull what appeared to be a long thread up high above her head and then swoop it back down and take another stitch and then repeat the process.
i wonder if it could be a form of self soothing like a baby sucking it’s thumb or a toddler rubbing a soft blanket with his fingers?
ive heard that the pencil coloring that has been popular for the past few years is relaxing. Your mom might enjoy that.

I think that sometimes it is just a habit. Some people around here sit with a toe on the floor and rock the heel of their foot up and down very quickly, for minutes and minutes at a time. Lecturing to a group, with half of them doing it, drives me potty. I don’t think it’s anxiety - possibly boredom, but I do my best to be interesting! Some people have verbal habits, like, that are equally annoying, and they don’t even seem to realise that they do it – like. I’ve heard people say that a compulsive need to knit or crochet comes into much the same category. Try not to get annoyed by it.