You may want to try tracking the behavior and see if you can identify a pattern to it or a trigger of some kind. Given your further description, it certainly sounds like it could be an expression of anxiety. So finding the trigger(s) or pattern might be very helpful.
I hope the child psych you're going to see is familiar with gifted kids and their special needs/issues. If you're not sure, you may want to get very specific in asking about his qualifications in that area - how many gifted or 2E children has he treated, any special training or education he has in that area. Even if you know this person, you may want to find out exactly what kinds of services he provides (treatment only, testing/assessment too or what?), if he only does treatment, who does he refer families to when he feels testing is needed and what child psychiatrists he works with when he feels a child needs a referral for medication or more complex diagnosis. You may never need this information but it's not a bad idea to get it ahead of time.
