Not sure if there is any evidence about closing eyes, specifically, but there is plenty of evidence (source that comes to mind is ON KILLING by Dave Grossman) of troops during this period aiming to miss---shooting over the heads of enemy combatants. And many muskets would be found with multiple musket balls still lodged in the barrel together; soldiers would pack a load, pretend to fire (and in the din and chaos, they'd hope not to be noticed), and then reload, pretend to fire yet again, and so on.

This reluctance to aim at other humans wasn't really rectified until the American military (someone else help me with other countries?) changed targets used in practice from concentric circles to humanoid. They also instituted a rewards system for making shots on those targets---forget the specifics, but increased privileges or R&R or etc---and later the targets themselves were made to go down, fall over like a person would go down if shot.

This apparently was a successful technique.

I don't think any training technique was ever able to eradicate the reluctance of nearly all soldiers to impale people with their bayonets, however. (It's been a while since I've read the book, so someone corroborate this for me?)