I look at people's mouths also (if I am looking at them at all). It seems less rude / dodgy than not looking at their faces, and also helps me make sense of what they're saying.
When I try to force eye contact, I either become too confused about what I was saying to proceed, or it's like staring at the sun. Or walking into someone's bedroom uninvited. It's overwhelming and feels too private. And also I can't figure out *which* eye to look in. When I watch other people converse with each other I am startled by the degree to which they do this. Do they have to look into each other's eyeballs to see each other? It seems weirdly over-intimate to me.
I sometimes look *at* someone's eyes, if they're an interesting color. But generally when they're looking elsewhere.
I'm very comfortable maintaining eye contact with my cats.
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Now a penguin may look very strange in a living room, but a living room looks very strange to a penguin.