One of the coolest things to remember is that because prey animals have eyes on the side of their head, they are looking at you when they're in profile, not facing you! Hot tip for artists and animal lovers!
Okay not really. The thing about animals with eyes on the side of their head: they DO in fact look directly at things and they CAN use binocular vision. I am going to use horse examples because horses are what I know best.
A horse uses binocular vision when it is trying to see something better - monocular vision gives a wider field of view but no depth perception and is not very clear.
When alert, the horse will look directly at something, facing it, using binocular vision to determine what it is and whether it is a threat.
A general rule of thumb with horses is that whatever their ears are pointed at is what they are looking at.
In the first image, the horse is looking at me. In the second, she is not.
In this set of images, she is investigating that blanket. You can clearly see her head pointed at the object and she examines with her binocular vision and nose.
Now, in this case, the horse is looking at me without his head facing me. You can tell he's looking at me with his monocular vision by how he has one ear facing me.
In most of the professionally done horse reference pics you see, the horses are going to have their ears pricked up and alert and be using their binocular vision. Why? Because it just looks better. How? Either the horse is investigating/curious about the camera or person holding the camera OR someone standing where they want the horse to look has just snapped their fingers or whistled or waved an umbrella or something to get the horses attention.
I just find it silly to say that the prey animals are not looking at you when facing head on, when the examples you gave do not seem to demonstrate that. To me, all of the squirrel and bird pictures look as if they are looking at the viewer - with the side view being a more 'relaxed/trusting' sort of look while the front view is a tenser investigation. The horse does not look like its looking at the view in either drawing - the first looks relaxed and looking somewhat to the side, the second looks alert and gazing directly in front of it.
I will add on for (at least some) birds.
This bird is not looking at you.
This bird is intensely looking at you
Many animals move their pupils. In both photos you can see her pupils, but they're only facing forward in the second.
Here she is intensely examining a chip in front of her face.
She is not looking at me- actually she's not really looking at anything she's listening to something she heard outside.
Peas most often look at things sideways when they need a wide field of view, too- like when they are scanning the sky for hawks, they will walk puffed up with their head tilted to the side to look up.
But when they want to actually look at something or someone, they will look head on as well. It's just that unlike animals with forward facing eyes, they don't HAVE to look at you head on.
