An Etymological Dictionary of the German Language/Annotated/Gleißner

Gleißner, masculine, ‘hypocrite,’ from the equivalent Middle High German gelîchesenœre, allied to older Modern High German gleißen, ‘to dissemble.’ The latter is from Middle High German glîhsen, gelîchesen, Old High German gilîhhisôn, ‘to dissemble’; literally ‘to be equal to any one’ (from gleich), equivalent to the Middle High German parallel form gelîchsensen. Compare further Latin simulare, allied to similis.