Benjamin does almost nothing in the story that turns on him, which is the point of him. He is the object the plot moves around: the one son Jacob will not risk after losing Joseph, and therefore the only lever the disguised Joseph has.
Joseph demands that the brothers bring the youngest down to Egypt to prove they are not spies, and Jacob refuses until the famine leaves no choice. Judah offers himself as surety, in terms that hold him personally liable forever. In Egypt Joseph seats the brothers by age, which unsettles them, and sends Benjamin five times the portion the others get at the meal, watching to see whether they resent the favourite the way they once resented him. They do not.
Then he has his silver divining cup put in Benjamin's sack, has the caravan stopped and searched, and declares that the man in whose sack it was found will be his slave and the rest may go home free. It is the same choice they faced with Joseph, arranged deliberately: abandon the favoured youngest son of Rachel and walk away clean.
Judah answers with the longest speech in Genesis, describing his father's state, the surety he gave, and offering to be enslaved in the boy's place. Joseph cannot keep the disguise through it, clears the room and tells them who he is.
The test needed a passive subject to work, and Benjamin is it. Nothing he says or does affects the outcome; what matters is whether his brothers will pay for him.