First of all, intransitive selection “become” figures not so much to be a plain ordinary copula as the fientive verb, synonymous with prepositional construct “turn into”:
1. To play the character well, you must become him in your imagination.
2. To play the character well, you must turn into him using your imagination.
Both English diction and grammar seem heavily influenced first by continental Norman French langue d’oïl and, somewhat later, indigenous Anglo-French during the Middle English period from 1066 to the fifteenth century of notable author William Caxton 1415-22 born to 1492 and official Chancery Standard of King Henry V 1413-22. Now highly frequent use of disjunctive pronouns can also be very well said to characterize French grammar & composition, such as the object moi pronoun found in quaint Modern French expression c’est moi “It’s me!”:
1. To play the character well, you must become him in your imagination.
2. Que jouer bien le personnage, on doit lui devenir en l’imagination.
Here disjunctive or stressed mod.Fr pronoun lui “him” agrees with the indefinite subject on “one, you etc.”