Why is it that evil characters are sometimes drawn without eyes? One example is Saki Arima in Your Lie in April. I have seen others from time to time. Any thoughts?
Have you ever heard the phrase "The eyes are the windows to the soul"?
One of the first big names in manga and anime, Osamu Tezuka, developed an art style in many of his works where the eyes of characters were abnormally large, because it was easier to make them expressive to show emotions - as discussed in this answer and this Quora article.
So, what happens when you reverse that? If you make a character's eyes small, then it becomes harder to discern their emotions, and harder to make an emotional connection with them (and before someone brings up, say, Brock from Pokemon, note that while his eyes are permanently squinty they're also pretty big). By taking a character's eyes away completely, you are completely severing that emotional connection, and to some extent, you are giving the impression that they are emotionless - which is often what is being expressed, since the eyeless face is used on characters that are either acting in a sociopathic manner (lots of school bully-type characters are depicted this way), or who are otherwise emotionally distant or disconnected, like Arima Saki in Your Lie.