I read that same book years ago. Sakai’s near-death flight back to his base at Lae, wounded as he was and though an enemy combatant was amazing.
Yes he was shot through the eye by the tail gunner on a Dauntless. A .30 cal. bullet through the eye would stop most people but Sakai made it back home even tho he was passing in and out of consciousness.
He was based at Lai and I remember him saying at one time that a fellow pilot told him American Marines had landed on New Guinea and were fighting like demons.