It's the protagonist's mother reacting to the protagonist's boyfriend's mother chastising the protagonist. “I hope you’ve learned your lesson,” she said to me. Mom took a step forward, putting a hand on my wrist but looking Zania in the eye. Things erupt a bit after that.
I would go with the lover/father thing. When you look into someone's eyes, (plural) it's in a loving, sensual, almost explicit way (and yes, you can look into someone's eyes, you constantly - but with minute movements - flick from one eye to the other) but when you look someone in the eye, it's more of an expression which conjures up a beady eye, the eye of suspicion, as if you are looking at them through a suspicious or questioning squint.
Yes, this, and if someone says, "Look me in the eye!" it's generally a superior demanding an inferior's sole attention to the message the superior is about to lay down . . . or it's someone wanting to see if the other is lying to him.
This is kind of fun. As you go through your day, make a mental note of every time you make eye contact with somebody. Even if it's just a brief occasion. What are the feelings you have at that moment? It's a great writerly exercise. Eye contact produces a heightened response, no matter who the other person is. If you make eye contact with a stranger on the street, you're more likely to remember them. If it's pleasant, and they say 'hello' as they pass, you will probably feel a little burst of well-being. If it's not pleasant and they stare at you and say nothing, you will feel uncomfortable. Same with people during the day. If you make eye contact, you will be more aware of what they are thinking and feeling. It's a moment of subliminal communication. Fun stuff, if you pay conscious attention to it. "Look me in the eye," is an expression that doesn't so much mean "establish eye contact," as it does "stop shifting around and deal with me honestly." It's more an expression than a real experience. As a writer, I would approach it that way.
I used to work with a lady that had what I call lazy eye, which may not be the correct term, but one eye was aimed in a different direction than the other. When I tried to look at her in the eye it was very uncomfortable and Jack Asher's comment was really the only solution. I know this is not really addressing the question but it would be unnerving for a person with that condition to ask you to look them in the eye. I would give my character an eye patch or make them a Cyclops to get around the dialogue. Then there is "Pan's Labyrinth" with the eyes on the hand solution.
Oh gosh that scene freaked me out. I couldn't get it out of my head for days. I finally managed to shake off the creepy feeling because my friend wanted to watch the director's notes, where the actor in the Pale Man's costume was sat in a chair with make-up brushes waving around his face, and some other guy came up from behind and said something like, "Hey Chris, want a cup of tea?" And the Pale Man shifted slightly and said something like, "Yes. No sugar, please!"
In my native language, using the singular would have a funny but naughty connotation. And so, I have the habit of using the plural in english, as well. But when I'm reading, in english, it makes no difference in terms of connotation, although it the plural still sounds more natural to me.