Final answer:
The pronoun 'his' is used as a Predicate nominative, renaming the subject 'plan' as belonging to someone.
Step-by-step explanation:
The pronoun 'his' in the sentence 'The brilliant plan was his, not mine' is used as a Predicate nominative. A predicate nominative is a noun or pronoun that follows a linking verb and renames or identifies the subject of the sentence. In this case, 'his' renames or identifies the subject 'plan' as belonging to someone.
Learn more about The use of pronouns as predicate nominatives