Left eye radical - pictograph of an eye rotated vertical, with the pupil shown as the inner stroke. Indexes 眨 in the vision family alongside 看, 睡, 瞪, 眯. Eyes blink, doze, glare, squint: 目 marks every verb of eyelid motion.
Right 乏 supplies the sound fá -> zhǎ through an irregular shift. The 'weary' meaning of 乏 also lends a faint semantic flavour - a blink is the eye's tiniest moment of rest, the eyelid briefly dropping the way a tired body does.