A Straight Line Running Through the Eye
This looks like the ideal candidate. The eye has structure. It has a lens, retinal cells, and they all lie on different parts of the eye. We define direction this way: the retinal cells are further back than the lens; the lens are further forward than the cells.
Further, lens and cells make a line so that we can say what lies off that line is to the left/right/above/below of the line. If we define direction relative to this structure, it seems to survive every counter-example so far. If I turn my head, my eyes, bend one out the back of my head, relocate my self, still: retinal cells lie further back than the lens, and the lens lies at the front.
However, there are still problems, indicated by the following questions:
(1) There are many lines in the eye; the eye is an ovoid; none obviously stand out. Why pick this line running through lens/cells? Why not pick ‘front’ as what lies orthogonal to that line — to the side of the line?
(2) It’s a straight line. But there are many straight lines passing through the eye.
(3) What makes that line straight rather than crooked or curved?