Which preposition to use with flapper

across Occurrences 1%

" The Mock Turtle sighed deeply, and drew the back of one flapper across his eyes.

in Occurrences 1%

This is probably an allusion to the flappers in Gulliver's Travelsthe servants who, in Laputa, carried bladders with which every now and then they flapped the mouths and ears of their employers, to recall them to themselves and disperse their meditations.

Which preposition to use with  flapper