Behavior analyst would try to redirect him and praise any efforts of him stopping with the demand to keep hands down repeatedly. Get some sensory toys like the stress foam balls, squishy water filled snake thingys, playdough, shaving cream to write in , rice/beans bin, water table with water toys to squirt, rubics cube..hand held water games with buttons, small magna doodle to draw and distract him at restaurants and in car, grocery store. We never had this one behavior but with others we just redirected her to more appropriate things to do with hands, feet and praised like crazy when she attempted to stop it..and always kept the demand " hands down" or "feet down' or whatever behavior you are working on. OT/PT probably have some more ideas than me. It is probably done when he is bored or anxious so see what he may be feeling when he is doing it and take note. Good luck!
Shelley
More than a "hand" stim, this is a visual stim (side glancing) at least in the way that you have described.
I have read that cod liver oil is a very good supplement to give for visual stims as it is believed that they are caused by a vitamin A deffeciency.
After reading that it greatly reduced or completly eliminated side glancing in about 2 weeks in other kids, I began giving it to my son when he was a little over one and had just barely started experimenting with this type of stim. I remember I didn't even know exactly what was going on with him yet, but thought CLO was harmless enough (and actually just good for you) to give it a try as I knew the behaviors he was showing just weren't right. He does not have this time of stim as of right now, he is almost 2.
Try adding magnesium to his diet