Thank you for your query,
Shaking of arms and hans associated with eyes staring looks like a seizure
But seizure episodes will be unpredictable and they wont be produced by voluntary actions like eating.
Some times tremors also will present like this, especially action tremors, they absent in sleeping and usually present when child is doing work with hands.
So child needs examination and if possible video recording of the child during the abnormal movements by a mobile will help the doctor to come to a conclusion.
Any how EEG will rule out most of the types of seizures.
Hope I have answered your query.