I'm sorry I don't have an era or time frame for this. It's been a few years since I was told the story. But basically, if one eye is blind folded, in sudden darkness the shift in light could let their un adjusted eye see much better than the other one.
A plausible explanation could be that the blindfolded eye would be instantly adapted to low light conditions; say, when entering a building. The adaptation normally takes 20 to 30 minutes but assasinning people probably can't wait that long.
There have been some theories that the pirate eye patch trope might have similar backstory: if you're boarding a ship in daylight but want to have a quick romp in the hold (where it's dark) without being effectively blind for the first minutes, you might want to blindfold one eye beforehand.
As I said, this is a plausible explanation especially since blindfolding or patching one eye to retain low light vision is still done occasionally. I did it in the military for example. But as far as I know, there is no hard evidence that assassins or pirates did it for this reason.