You will learn to tell a look that invites from a look that presses, and stop translating your cat's eyes through a human grid.
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A cat that stares at you for a long time is taken for an affectionate cat. In its own language, a held stare usually says something else.
Between cats, long eye contact is not a tender exchange. It is pressure. Whichever one looks away first usually avoids the confrontation, and that outcome suits both of them.
So when you stare at your cat to show it you love it, you are using a signal that belongs, in its grammar, to another family altogether. Most cats living with people get used to it. That does not turn the signal into a gift.
A cat staring at you from across the room is often asking for something specific: that you stand up, that you open a door, that you stop what you are doing. The look is a request more than a declaration.
Closing the eyes slowly in front of another creature is, for a cat, an act of disengagement: I see you, I am not threatening you. Many cats return it to a person who offers it.
The mistake is to fire it off like a cue and expect a reply every time. If it does not answer, it is neither cross nor indifferent. It may simply be busy elsewhere.
The gesture is worth most for what it makes you do: slow down, soften your face, stop staring. That combination is what it picks up, more than the eyelid on its own.
A pupil opens when the light drops. That is the first explanation to rule out, ahead of any emotional reading. A cat with very round eyes in a dim room tells you almost nothing.
Under steady light it is different: a sudden widening often goes with a rise in arousal or alertness. The key word is sudden. The change informs you, not the size.
Always compare in the same spot at the same hour. A lasting difference between the two pupils does not belong to this grid at all, and should be shown to a vet.
A cat that turns its head as you approach is often making the most courteous gesture in its repertoire. It is taking the pressure off.
We read it as disinterest because, for us, turning away closes the conversation. For it, that move is sometimes what makes the conversation possible.
A simple test: turn away yourself, sit down, busy yourself with something else. Plenty of cats come over within the minute, precisely because nobody is looking any more.
Position matters as much as the eyes. A cat sitting still in a doorway keeps an exit open behind it. That is an observation post, not hesitation.
What it is weighing up, usually, is the cost of coming in: the noise, the visitors, the dog, the stretch of floor to cross. It is not avoiding you, it is costing a route.
What helps is not calling it but lowering that cost: turn the television off, clear the corridor, leave a second way out available.
Many of the good moments with a cat involve no face-to-face at all. You are in the same room, both turned towards the window, the street, nothing in particular.
That shared attention on a third point is a form of company cats accept far more readily than an exchange of stares.
If your cat sits near you without ever seeking your eyes, that is not a thin relationship. It may be the shape it prefers.