lol You must have seen the pic I attached .
then I have a responsibility to account for it.
手招きする＝to attract or beckon with hand
手が動く= The hand is movable.
招き猫= this is cultural stuff in Japan , It is similar to 達磨 and 熊手, and it is regarded as the stuff to attract customers , patrons , happiness 商売繁盛無病息災 etc. so You can often see the stuff in the retail store or traditional type restaurant if you come here for sightseeing .