When Brian Burke, after four pressure-packed and unsuccessful seasons as general manager/president of the Toronto Maple Leafs, was abruptly fired on Jan. 9, it might have been easy to assume the 57-year-old would want to take some time off. Maybe just go to the Caribbean and relax. Hardly. “I’m not much for sitting on beaches,” said Burke in a phone chat from Toronto yesterday. “At my press conference (after his dismissal), I was asked if I wanted to be a GM again. I said, ‘Yeah, tomorrow.’ ” Under the incessant demands and scrutiny of ownership, fans and media, Burke worked hard to build his team — yet it never made the playoffs during his tenure. But now, the team he assembled is suddenly playing well, and it’s looking like the Leafs could return to the playoffs for the first time since 2003-04. Toronto took a three-game win streak into last night’s game against the Bruins at the Garden, and was fifth in the Eastern Conference at 15-9-0. Whether Burke is angry, frustrated or proud about the Leafs’ performance is anyone’s guess. He is adamant he said what he wanted to say at his exit press conference and will say no more.