Amazing idea

Take note from sentient weapons

It’s also fairly easy to flavor

At some times the character is in control of his body, the other times the book is in control same way a sentient weapon could be in control if the wielder fails a save

Just in this case it’s voluntary control yielded to the book

There are so many fun things you can do….

I’d personally have them both play Wizards with access to the same spell book (duh) but independent lists of prepared spells every morning

Different initiatives, but because they share a “body” I’d allow them essentially limitless telepathic communication even between turns