The small autistic children that I see sometimes have this apparently odd behavior of running with their eyes averted. They either look to the side, look down, or close their eyes. They do not do this while walking. These children are under three years old, and do not have the capacity to say that something is wrong with their eyes.
I have started to wonder whether the behavior is a compensation for the inability to change focus as they run toward things, or whether the constant problem with focus is causing them to have a sensory disturbance of another kind. I think that a focus problem can be assessed by a clever pediatric eye care specialist.
Another important thing to consider, if my hypothesis about the behavior being related to a vision problem is correct, whether other seemingly atypical behaviors might be related to another problem or problems.