While it is true that Clinton made excellent use of late-night talk shows including Arsenio Hall and even more to the point, Johnny Carson (though that's a tale for another time), a better example and one far more applicable to Trump happened quite a bit earlier.
When people think of Nixon and television, there is a tendency to focus on the debate with John F Kennedy. That provides a horribly lopsided picture. Nixon used the medium brilliantly with the Checkers speech and did awfully well with Jack Parr.
Here was the great loser attack dog of the Republican Party, a figure best known for scandal, defeat, and perhaps the most petulant exit line of any American politician, sitting in America's living room, making relaxed and charming conversation, and not only playing piano, but performing his own composition.
Parr himself would later write:
He had been on the Tonight program with me, and against his own judgment and that of his many advisers, I got him to play the piano. It was an unusual moment, with Richard Nixon playing a ricky-ticky tune that he had composed. Marshall McLuhan, the media analyst, had written in his first book that if Nixon had played the piano on the Tonight program in the 1960 campaign, he would have won the election.
RICHARD NIXON ON "THE JACK PAAR PROGRAM" (MARCH 8, 1963)