Green’s Dictionary of Slang

to disregard and dismiss what has just been said.

1894		Hamilton Eve Jrnl (OH) 3 May 2/4: Bristley got up on his feet and winked the other eye.
1902		Bulletin (Sydney) 25 Oct. 14/3: At the opening of the State Reform Parliament (Oct. 15) it was hard not to wink the other eye at the so-called ‘Reformers’ who, lolling in the lap of luxury themselves, menace the poor little ‘perks’ of railway porters, and shake their heads ominously at old-age pensions and free education.
1903		Ade People You Know 40: At which Mother would wink the Off Eye and murmur, ‘Is that so?’ with the Loud Pedal on ‘That.’.