Product review (4 stars): IceMaker works for Kenmore Side-by-Side - Model -- 106.56586500
I've got a Kenmore side by side (106.56586500) and it installed just fine.  The only reason I rate it 4 stars instead of 5 stars is that the instructions leave a lot to be desired. Luckily, I referenced a video on appliancepartspros.com and it explained the whole installation.  I ended up using my old wiring-harness and I used the old wire-arm (this kit did come with 2 wiring harnesses - none of which would have fit).  Otherwise, it fit just fine.  Reference an installation video on the internet and it's fairly easy to install (20 mins or so).  I'm pretty happy with the price because it was about 1/2 the price of what Sears would charge !