This is the explanation that makes the most sense to me so far. So the eye that hurts first while a source of light is flickering, be it a display or ambient light, is probably the eye that normally doesn't get used that much? And perhaps it is that eye that should be used to view when doing the eye patching we are talking about currently.
Only thing that contradicts this theory a little, at least at first glance, is that the eye doctors have not found a dominant eye for me. It seems my eyes are used equally. When I do the Miles test (folding hands in triangular form), I don't find a dominant eye myself. And when I do the Porta test, I always see both fingers and thus can't cover the distant object at all.
But still, this theory makes a lot of sense and can at least explain certain kinds of eye strain.
Edit: I wonder, could a certain light spectrum wake up the suppressed eye, too? Without any flicker, just having a certain spectrum like White LED.