your picture still looks like it might be cross eyed - but maybe because the picture is not from directly in front
yes it is a good idea to model the socket around the eyeball
But if your model pokes through the mesh when you move the eyes (and your pivot is in the correct spot) then it is a problem with the mesh not a tracking problem.
Sorry to reiterate, but your eye’s in “real life” do not both track to the same point.
the reason an object is in focus is because the muscles in your eye control the lens in your eye to focus the light onto the retina. The middle part of your retina is more sensitive than the outside (which is why your peripheral vision is blurry).
Imagine looking through a window at a tree - then (with out moving your eyes) focus on the glass that you are looking through. Your eyes have not moved - only your lens
I know it is hard to imagine but your eyes do point in different directions. It is roughly the same point but not exactly. (a more extreme example is a person who has a lazy eye - and yet they only see one image)
How is this so?
Your brain does amazing things to make the 2 images it receives “look correct”
Here are a few examples of what the brain does to correct an image
Look directly into a mirror - then tilt your head to the side
do you notice what your eyes do? - yep, they rotate sideways!
its only a few degrees and it’s an involuntary muscle reaction but it happens
this is your brains response to “fix” the rotated image being sent to the brain.
so what about when you tilt your head further?
say you’re watch TV lying 90 degrees sideways on the couch
The image appears upright because your eyes rotate as far as they can go and then the brain corrects the image to display the way it should.