In episode 10, Ae-Sin is studying words starting with letter S, she already know Sad ending and learned the word Stranger. Ae-Sin says the every word starting with S has sad meaning. But her helper disagrees and enumerates Snow, Sunshine, Star and Sky, and asked what is her favorite among them. And then, while Ae-Sin is walking and thinking of the words such as Mister, Stranger and Sunshine, Eugene and Ae-sin saw each other from different side of train railways, And Ae-Sin whispers to herself, Mr. Sunshine.
That's my thought about the title.
But I also agree on every key scene, Eugene is standing on the sun or light. Like on the first time they saw each other as snipers, the lamp on the streets lighten up like a sunshine. And also in American legation where they cover each other face, the sunshine there brought the scene in different level.