One requirement for a smile to be sincere, is there has to be dynamic momentary partial closure of the eye lids. Without a partial eye lid closure, the smile is insincere. Period. I wish to strongly emphasize that this does not mean the person as a whole is insincere - merely that in that moment, regardless of what their mouth looks like or what words are being spoken - they are having to "push out" what is known as a "Social Smile" (Ekman). They are acting happy (or happier) than their true emotions in that moment.
Here are two images of Brad Pitt's eyes. The mouth's were similar in the original photos - but I wanted to isolate his eyes for a great nonverbal teaching point.
When a sincere smile is made, the eye lids partially close - but it is primarily a secondary, passive closing. This closure is caused by a contraction of the orbicularis oculi (pars orbitalis) muscles which, in a sincere smile are always subconsciously controlled. This muscular contraction causes the lower lids to bunch up in a very characteristic fashion creating a concave-up furrow (crease) in the lower eye lids. This is wonderfully exampled in the image above.
In contrast, the photo below shows Brad Pitt at the same age, with his eye lids are closed in an identical amount. Notice that there are no creases/furrows in his lower lids in this image though. This is because a different muscle is being used to close the lids - the orbicularis oculi (pars palpebralis). This is consciously controlled in a forced "social smile" and thus even when great actors are "trying to smile" - they often have a difficult time doing so. This is why method acting is so valuable.
In conclusion, not only must all sincere smiles have partial, momentary partial eye lid closure - you must see this characteristic furrow in the lower lids as well. Otherwise - the smile is NOT sincere.