Welcome, Nils, to the Boards. Darn good question you ask, and I’ll give it a shot, although I’m no opta–opto–aw, heck, eye doctor.
Squinting doesn’t hurt me at all–I do it all the time when I’m outdoors and the sun’s out. I’m dead sure I’m doing it on purpose, because if I don’t, it hurts my eyes. Same thing happens when I get up in the mornings before dawn; I turn on the light and I have to squint to see anything. It hurts like crazy to have a lot of light hit the retinae and squinting filters out enough that I can get dressed and drag myself to the shower.
And the reason both eyes move together lies in the brain, specifically, our visual cortex. Unlike chameleons, humans can’t process two visual images at the same time. Our brain forces the two eyes to work together.
Now, let’s wait till someone smarter comes along and explains this in better detail.