I would guess that the person operating the puppet (yes, he isnt a real being - sorry) is using one arm in zippy's 'arm' and the other inside the head operating the head movements?
I assume it would very cramped more than one person operating it.
Nothing to do with the question , but I can't resist saying that I once attended a talk given by a man who spoke exactly like Zippy fron 'Rainbow'. To top it off he even looked a bit like him (bald, with a big mouth)! Can't stop laughing thinking about it now... happy days.