MIAMI—Former Vice President Al Gore on Tuesday returned to the campaign trail in Florida, where his 537-vote loss cost him the White House in 2000, presenting himself as “exhibit A” on the importance of voting. “Please take it from me: Every single vote counts,” he told 1,600 people at a rally here with Democrat nominee Hillary Clinton. Mr. Gore reminded younger people in the audience that his loss to Republican George W. Bush was “very close”—so close that many Democrats believe the outcome would have been different if the Supreme Court hadn’t halted a recount of ballots.