Serving a sovereign and serving a parent are one and the same principle;

Four characters and four characters across a semicolon, and the next unit is four and four as well — but the two are not the same shape as each other. This one is a topic followed by what is said about it; the one after is two parallel clauses that apply it. Matched depth is not matched form, and the two stay apart.

You for a parent's kindness, and I for a sovereign's."

為 is wèi both times, for the sake of — not the wéi of becoming. Eight characters, perfectly balanced, and they settle the whole argument by refusing to decide it. Neither death is the sadder; they are the same duty pointing two ways.

This is just the case:

The cue, three characters, and what follows is the pair of lines the scene has been building toward since the first tear.

Weeping eyes look upon weeping eyes; a heartbroken man sees off a heartbroken man.

Each line repeats its own four characters on either side of a single verb, so the grammar itself does what the sense says — two identical halves facing each other across a stream. 斷腸, the severed gut, is the standing Chinese image for grief where English says the heart. The lines are old and were not made for this book; the novel has borrowed them because nothing it could write would fit better.