1580s, perhaps from Middle Dutch blinken "to glitter," which is of uncertain origin, possibly, with German blinken "to gleam, sparkle, twinkle," from a nasalized form of base found in Old English blican "to shine, glitter" (from PIE root *bhel- (1) "to shine, flash, burn").
Middle English had blynke (c. 1300) in the sense "a brief gleam or spark," perhaps a variant of blench "to move suddenly or sharply; to raise one's eyelids" (c. 1200), perhaps from the rare Old English blencan "deceive."
Originally with a vague and shifting set of meanings, many now obsolete, having to do with motion of the eyes; in earlier use "the notion of 'glancing' predominates; in the latter, that of 'winking'" [OED]. Meaning "cast a sudden, fleeting light" is from 1786; that of "shut the eyes momentarily and involuntarily" is from 1858. Related: Blinked; blinking. The last, as a euphemism for a stronger word, is attested by 1914.