The element at bottom is cloth. The element on top was originally two sets of intersecting lines. The combination indicates a long piece of fabric with fine cross-stitches. Scarce and rare are associated meanings, via "fine." Desire is an extended meaning, in the sense of a longstanding desire of a kind rarely obtained.
adds sun/day to suggest the drying out of a cloth by means of exposure to the sun. Thus the meaning dry out.
adds eye to suggest "gaze at a fine, dimly visible object." Yearn for is an associated meaning (yearn for something far off, dimly visible).