An Etymological Dictionary of the German Language/Wink
Wink, m., ‘sign, wink, nod, hint,’ from the equiv. MidHG. winc (k), OHG. winch, m.; allied to winken, vb., ‘to wink, beckon, nod,’ MidHG. winken, str. vb., OHG. winchan, wk. vb., ‘to move sidewards, totter, nod, wink’; corresponding to AS. wincian, E. to wink. If ‘to totter along, move with a sideward motion,’ is the primary meaning of the Teut. root wink, the Aryan root may be the same as that of weichen (wī̆g, wī̆k). Related to the following word.