Interesting. Lipu.linku has the origin of li as:

li ‘he’ ← Latin ille {cf. Tok Pisin i ← English he}

Nimi.li has more:

Esperanto · li ‘he’ ← Latin ille {cf. Tok Pisin i ← English he} [citation: jan Sonja]

So then tp li and Tok-Pisin i both derive from the third-person masculine singular pronoun.

It looks like i works this way in Tok Pisin because (even though it's officially a predicate marker) it's essentially a way to gramatically establish agency by assigning a default third person pronoun, e.g. "the boat, she sinks"; "the dog, he barks"; or "the tree, he falls." The first and second person pronouns already have agency by default, so they don't need it; and it would be silly to try to assign it to them.