WordNet records no synonym and no antonym for eye contact. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a meeting of the eyes between two people that expresses meaningful nonverbal communication
“it was a mere glance, but the eye contact was enough to tell her that he was desperate to leave”
contact that occurs when two people look directly at each other
“a teacher should make eye contact with the students”
Synonyms, antonyms and the broader and narrower relations for eye contact come from Princeton University’s WordNet. Full sources and licences.