Why does closing one eye in bright light allow me to open the other?
A couple of factors play into this. First, you're halving the number of nociceptors that are signaling the brain. Second, there is a psychosomatic effect. Your brain continuously combines the visual data from both eyes to form one image. With one eye closed, your brain combines the brightness of both inputs to form an image that is roughly half as bright as reality. As a result, your brain not only ignores a portion of the nociceptor signals from the open eye, but it also doesn't assume the presence of pain like it normally would.

I've no publicly accessible sources to cite, as this is something I learned in my EMT class. Someone actually asked your same question in class