When J.D. Vance did his initial walk-through of the Republican National Convention stage this week after he was named Donald J. Trump’s running mate, the Ohio senator was joined not just by aides and event organizers.

He was accompanied by a man who had pushed behind the scenes as hard as almost anyone to put him on the ticket in the first place: Donald Trump Jr.

When they each deliver a prime-time address on Wednesday night, the moment will mark not only Mr. Vance’s national debut but the unquestioned arrival of Donald Trump Jr. as a political force to be reckoned with in his own right.

The younger Mr. Trump is now the rarest of political creatures: a top confidant not only to the Republican presidential nominee but also the vice-presidential nominee. Soon after Mr. Vance got the call from the former president that he would be on the ticket, one of the first outbound calls he made was to the younger Mr. Trump to thank him for his help, according to a person with knowledge of the call.

“Don is a power player and I think anybody in Republican politics is realizing that he’s on a list of five of the most powerful conservative voices and influencers alive,” said Charlie Kirk, a close Trump ally who co-founded Turning Point, a constellation of influential groups on the right, and who hosts a popular streaming show.

The 46-year-old eldest son and namesake of the former president did not enter the first Trump White House in an official role. And he said in a brief interview on Wednesday that he would not serve in a second.