The moment lasts about 45 seconds.

But in it, so much of the cautious stagecraft that surrounds and inhibits Hillary Clinton appears to break away.

Mrs. Clinton, pelted by a driving rain and seemingly overcome by exhaustion, exhilaration and a swirling wind, lets loose with her hands and relinquishes her script.

She skips past a critique of Donald J. Trump, flipping the page in her binder, and races to her closing lines.

“Here’s what I want you to remember,” she tells the crowd at a rally on Saturday in Pembroke Pines, Fla. “I want to be the president for everybody: everybody who agrees with me, people who don’t agree with me, people who will vote for me, people who don’t vote for me.”