The eye is the window to the soul. Don’t let anyone tell you that’s just a saying. Some prophetic people can look into a person’s eyes and see images flash before their mind of the person’s pain, joy, history, etc.
Speaking from personal experience, I look people in the eye when talking business, but I’m always ultra sensitive to whether they’re comfortable with extended eye contact. My goal is to bless the person, not intimidate or annoy them.
I don’t know how the experience is for everyone, but eye-to-eye contact is extremely powerful for me. Sometimes I feel embarrassed, as though I have just trespassed into someone’s personal space by looking them in the eye. I’m embarrassed for their sakes because I wouldn’t want someone reading my mail (at least I wouldn’t have at certain points of my life).