Most Helpful Guy
I don't think we have conscious control over HOW we smile.
If it's genuine - the eyes are involved (according to both your source and what I've read in the past).
If it's not a genuine smile I think it's hard to involve the eyes willingly.
You might be able to con a smile with the eyes but as humans, our intuition is pretty good ;).
Also - I believe when we talk about smiling eyes, it's referring to the creases on the outside of the eyes, not the eyes themselves (although they have their own charm too!).