In Gillman's "The Yellow Wallpaper," the narrator is unreliable because she suffers from postpartum depression—at the time when no one knew anything about it or treatment. The information the reader gleans comes from the observations of the narrator. As the story progresses, however, the narrator's descriptions become less reliable because she is suffering more deeply from her illness.
The unnamed narrator sounds perfectly normal when she disagrees with her husband's "non-treatment" of her illness (he's a medical doctor).
...and perhaps…perhaps that is one reason I do not get well faster. You see, he does not believe I am sick.
As she fights her "imprisonment," the narrator has a better sense of what she needs than her husband does. She is a fighter, a woman standing up to the expectations and limitations of a male-dominated society. Perhaps as a way to defy her husband's repression and control, the woman breaks the rules:
I did write for a while in spite of them; but it does exhaust me a good deal—having to be so sly about it, or else meeting with heavy opposition.
Each day locked in her room makes her sicker. She sees faces in the wallpaper. By the story's end, she has lost her connection with reality:
The front pattern does move—and no wonder! The woman behind shakes it!
Sometimes I think there are a great many women behind, and sometimes only one, and she crawls around fast, and her crawling shakes it all over.
The reader should have doubts about how reliable the narrator is because of her instability—i.e., how much of what she writes can we believe?
In King's "The Border," the narrator is unreliable for totally different reasons: he is a kid.
When I was twelve, maybe thirteen, my mother announced that we were going to go to Salt Lake City to visit my sister...
The perceptions of one so young are questionable. He can only see what occurs around him through the limited lens of a youngster—unable to see beyond his limited years of experience.
The main conflict centers on his mother's pride. She refuses to align herself as a citizen to Canada or America, seeing herself as a Blackfoot, a Native American tribe of North America and Canada. She will not define herself by the white man's distinctions—the Blackfoot tribe has been around longer than those who attempt to control the boy's mother. So when she and the boy attempt to travel into the U.S., she refuses to declare her citizenship—she simply says she is a Blackfoot. Because of this, the U.S. border patrol will not allow her to enter; the Canadian border refuses to allow her to return to Canada for the same reason, and she and her son are stuck for several days between two countries.
The boy is unreliable because he is not mature enough to see that her concern is a matter of principle. He thinks she should just tell them what they want to hear—his heritage means nothing to him, but everything to his mother.
It would have been easier if my mother had just said "Canadian" and been done with it...
The boy is only interested in things that kids care about: food, the trip, etc. He is unable to concentrate on one thing for very long: he will speak about time spent in the past with his sister, jump back to the present, and then return to the past. His childish side is also seen in his willingness to believe everything he hears—he does not concern himself with facts. Because of these things, the boy is also an unreliable narrator.