The cause of eye irritation is no longer a mystery. It lubricates the cornea without blood vessels and secretory glands, but the closed eyes when sneezing have completely different reasons and are unexpected. Of course, there may be very few people who are squinting, but it is difficult for most people. When stimulated, the sneezing center of the brainstem commands muscle contraction from the esophagus to the sphincter, including the muscles that control the eyelids. Some people even squeeze a few tears when they sneeze.
It is impossible to sneeze with open eyes.