This is really strange. The icon should definitely be clickable by a right mouse button click to open a menu. What does the icon look like? Is it in gray scale or is it partly orange? (This indicates the state of the system).
There is another way to open the settings panel: go to the Start menu and type “Tobii EyeX Settings”, and open it from the list of search results.
After opening the settings panel that way, you could then follow the steps from step 4) in my first reply in this thread, and check what works and not.