Answer: to show how the narrator gets the idea for his trick.
Explanation:
In this passage, the narrator describes what having appendicitis felt like, because he had closely observed his half-sister. He kept all her symptoms in mind and he knew what he should feel like if he were to be "homesick".
We get a clue about this when he's saying <em>"my ancient half-sister (...) had actually had appendicitis"</em> - <u>unlike him. </u>
Consequently, the narrator knew what trick he had to pull if he were to be homesick.
