Which gives you more info? Looking in people's eyes or at their mouth? And if you look in people's eyes how do you get info on emotional state? Eyes do nothing for me in terms of informing me on emotional state. Following this line of thought can you really tell if someone might be lying though looking them in the eye? How? For me eye contact is painful and overwhelming. Makes me uncomfortable. But what is eye contact to you since from my understanding most don't experience that feeling when making eye contact?
It is the muscles around the eye and around the mouth, not the eye itself or the mouth itself. Maybe it will help not to look directly into the eyes.
Whenever you think of a smile, stretch your bottom lip, raise your cheeks, raise your eyebrows and try to pull back your cheeks towards your ears. Not with your hands just with your face muscles. You are opening your face, like a window or like opening your posture.
Muscles around the eye are part of a happy smile. Muscles around the mouth only indicate half of a smile. The cheeks also are part of the half smile but are only about 1/3 of the whole. For many people the ears move, too. My ears and scalp move when I make a full laughing smile. They move back.
You can smile with only your eyes, although this tends to affect your mouth as well. It usually means you feel nice or are suppressing joy. I exercise smiling with my full face, because if I only smile with my mouth then I don't get the health effects of a happy smile. Think of a smile as opening the face, because the eyebrows go up, and the bottom lip stretches, cheeks spread, ears spread, scalp moves back. It is analogous to opening a flower. The person is opening and is inviting, and their body expresses that openness in a physical way.
When you see a smile it should make you feel like you are smiling. You should feel warmth and an invitation. The natural thing to do is to open your face in return, unless you are unhappy, angry etc. In that case you can try to fake it or can be honest your expression.
Very often we are forced to pretend we are happy. At work I am constantly asked how I am doing. What am I supposed to say? I don't know most of these people, so I can't start talking about my personal situation. I say something like "Good!" and smile. They ask how I am doing, but it is not a sincere question. Its more like "Hello," and what they want is to know that we are at peace. It feels fake, and I don't like it -- but its how things are where I work. Its no big deal. I also get tired of saying the same thing all the time, so I try to change up my reply. It always has the same underlying meaning though. If I say "Well not so good today but maybe tomorrow" it is the same and means "You and I are fine. Carry on." They go on, and so do I. They forget, and I forget.
You can also smile a little with your posture. There is also open posture and closed posture. When a person enters a room of strangers with head down, they are perceived as uninterested and as evasive. They are using closed posture. They have frowned with their posture and have also shown either lack of confidence or confusion or that they are in a hurry...something like that. When they enter with head up, their posture means they are interested, open to people to speak to them and interact with them. It is like the smile and works with the smile. Walking casually is open, because it is associated with the things related to happiness. Walking fast is closed, because it is associated with things like stress. When people see you walk in a hurry, they will feel like you are closed. It is an intuition they feel that you are unavailable. Smiles are similar.