Looking at the node setup it seems the idea is you have multiple textures:
- body
- eye white (sclera)
- eye black (iris + pupil)
- eye mask, using red channel as alpha channel.
And the idea is that you draw the body, then the eye white, masked by eye mask, then you move the eye black some distance away from center in the direction of an empty or a bone or anything else controlling the eye movement, also masked by the eye mask.
Now, actually in your setup the eye white and eye black are combined together. Makes sense especially if the eye white is not a solid color and you want it to move together with the eye black.
Of course in actual shading the idea is implemented slightly differently:
- if you're outside of a mask, draw body texture
- otherwise draw eye black+white, with the coordinates translated by an empty (or bone etc.)
- you probably want to clamp the values to some maximum value, so the black doesn't go outside the mask (so it becomes invisible or travels into the other eye)
In the node setup below I'm using the vector difference (separate distances on axes) of the empty to the center of the cube, and vector-add that to the UV:


Unmuting the nodes will enable clamping:

It works only because I rotated the cube so it looks upwards and the X/Y axes of UV and object coordinates are aligned. You need to parent the empty to the cube in this configuration before rotating the cube, so that the setup works in any orientation of the cube.