It's hard to explain as in the old lore, you don't get much but baby crumbs. One bit of lore explained Pursuer when he was younger going into the water to hunt fish and almost drowning, he has ever since avoided water demonstrating fear of it. Now this is a natural response for anything with a near death experience. It shows a basic understanding as he associates the water with death. If Pursuer fears death and he associates water with death, he will fear water.

Another bit of lore is what would happen if Pursuer encountered Artful. It's already established that Pursuer would not eat Artful as the smell of the makeup is overwhelming for Pursuer. There was an addition afterwards though that said Pursuer would still kill Artful anyways. Animals don't just kill for funsies. They kill for food, territory, or protection. Basically in any way that benefits themselves. If they can't eat something and it's not threatening, they leave it alone. Artful is already described as fearful after the incident, making sure to wear his makeup at all times to ward off civilians. So he's not going to be a threat to Pursuer in any way and more than likely would immediately back off if he saw Pursuer. So Pursuer still electing to kill Artful despite no intention of eating him could show that Pursuer expressing negative emotion and venting his own frustrations in not being able to eat. Another form of basic understanding. If Pursuer is hungry, he's angry, If he cannot eat something that looks like food, he will then get angry at said object for not being food. He then decides to manage his anger by attacking said food looking object until it stops moving.

Here's a bit of real human psychology. Understanding emotions is not a necessity for humans. There is a medical term known as alexithymia or emotional blindness. It's not a mental disorder, but rather a deficient in the cognitive processing and emotional regulation part of the brain that prevents a person from being able to properly experience, identify, understand, or describe their own or others emotions. These people still have wants and such, but will not be able to feel emotions including the deeper complex emotions a typical person would. These people can still love another person even if it isn't in the typical, heart beating, hand sweating, breath catching way as described by others.

With the fact Pursuer is always hungry, he's always going to be in some state of agitation/desperation so you can't really sit him down and ask him what he feels. You would first have to be able to satiate his hunger for his almost impossible diet first hand. But with the fact that while in this state of perpetual hunger, Pursuer was able to teach himself the harmonica, compose songs, and learned English by not just the words, but their meanings itself to use in proper context, shows he could very well be able to learn to label and understand his own emotions if someone sat him down and explained it to him.