What you got there is the 'ol willy and sneaky Rainbow Wrasse. It was a great picture you got of him.
It's important to remember that Wrasses can change color, and quite quickly too; and they have different patterns depending on where they live. So they're not always going to match the pictures in the Humann/Deloach books, which are a great source, and can be quite confusing. It's no wonder you didn't find a match in the books.
The face markings on Rainbow Wrasses as a species are much the same. Notice the
blue stripe above the eyes, the
darker stripe below it that bisects the eye, and the
two blue lines immediately below the dark stripe.
The
red eye colors serve to differentiate from the similar Clown Wrasse, which also has different head markings.
Lastly, the dark splotch on the tail, while nearly gone in your photo, (it's more of a larger spot of the same colors) is still present, and helps mark the species.
View attachment 445116
Halichoeres pictus
View attachment 445117
Rainbow Wrasse - Halichoeres pictus - Wrasses - - Caribbean Reefs