The man identified these days as President Trump’s lawyer seems vaguely familiar. It’s in the way he feigns genuine laughter. How he clasps his hands. How he widens his eyes, as if he’s just been handed a birthday cake with a firecracker for a candle.

He is, of course, Rudolph W. Giuliani, whose public utterances of late have people debating whether he is a shrewd manipulator of public opinion or just — befuddled. But all agree that he relishes the limelight, every microphone a corkscrew capable of unleashing the spirits of his considerable id.

Indeed, he is working for the president free of charge.

There Mr. Giuliani was again on Thursday, opining from a Trump-owned golf course in Scotland while dressed in green-plaid golf togs bearing the Trump name. When a reporter from Sky News asked whether he thought that impeachment of President Trump was inevitable, Mr. Giuliani defended his client with a few provocative assertions before closing with:

“You’d only impeach him for political reasons, and the American people would revolt against that.”