For future reference, you will have better luck posting Illustrator questions in the Creative Cloud > Illustrator forums located here:
https://community.adobe.com/t5/illustrator/ct-p/ct-illustrator?page=1&sort=latest_replies&lang=all&t...
This forum is for Adobe Analytics.
However, this video may be helpful to you:
https://www.youtube.com/watch?v=bteUVmMUXkU
The eyedropper tool is a separate tool, you don't access it within the color picker window (or at least I've never seen it as an option, but the last version of Illustrator I used was CS4 which tells you how long ago that was)
Good luck!