Final answer:
The references provided do not contain information about a king who asks his wife to convince his friend to stay longer in Sicily. Without additional context or specifics, it is not possible to accurately identify the king in question.
Step-by-step explanation:
The question is asking about a specific narrative in which a king requests his wife to persuade his friend to extend his stay in Sicily. There's a number of texts that involve themes of kings, friends, and the setting of Sicily, but none of the provided references directly identify a king who asks his wife to convince his friend to stay longer in Sicily.
The reference narratives involve various historical figures, such as Cicero and Alcibiades, and other individuals like Sertorius and Alcée Laballière, but these do not align with the specific query posed.
Therefore, based on the given excerpts, we cannot conclude with certainty which king is being referred to in the question. It is important to note that for historical or literary inquiries such as this, precise context is key to providing an accurate answer.