I'm not sure exactly when or how the squiggly-line shape came about, but I do know there is an alternate notation that looks like a backwards eighth-note rest (called a "semiminima rest", as guidot mentions). You can see this shape used in Baroque manuscripts. I believe this form evolved into the familiar squiggly line during the baroque. My reason for this is a quick cursory glance at some Baroque manuscipts I found with a Google image search.

First, at the top of [this page][1] is an  image of a Corelli manuscript that shows the backwards-eight-note style of rest (marvel at his neat handwriting). Look at the first bar of the basso continuo part (second staff). Note the quarter rest is somewhat gamma-shaped, exactly backwards from the eighth-note rests on either side of it.

Next, look at this [scribbled Bach manuscript][2] of BWV 995. There are several quarter rests scattered throughout, especially in the second staff. They look a bit like square-root symbols. The gamma shape has gained a small check at the beginning, and the upward stroke -- *possibly difficult to write using the pens of their day* -- has now become slanted. the bar across the top is slightly curved.

Finally, look at [this neater manuscript][3] of Bach's Quodlibet from the Goldberg Variations. In the first full bar, the soprano part begins with a half rest followed by a quarter rest. The quarter rest is a horizontal squiggle, that almost looks like a trill or similar ornament. On the one hand, this symbol can be correlated to the square-root shape in the previous step, by emphasizing the angular check, shortening the upward stroke, and greatly curving the top bar. On the other hand, this symbol looks not terribly dissimilar from a modern quarter note rest, but rotated on its side.

Just a caution: this is all speculation on my part, but it seems that the evolution of this symbol was, at least partly, driven by the limitations of the pen technology of their time. I understand that pen nibs work much better when pulled, rather than pushed.

  [1]: http://bernardgordillo.com/sonata-for-viola-da-gamba-in-d-minor-op-5-no-7-by-arcangelo-corelli/
  [2]: http://www.jsbach.net/images/bwv995.html
  [3]: http://www.jsbach.net/images/quodlibet.html