In short, anyone who tells you that the Senate can vote to disqualify a current occupant of the office is simply wrong, and has not thought this through.
“OK,” I can hear you say, “but doesn’t the person being impeached have to be in office at the time of conviction?” No, and any other result would create an absurd result that the Framers could not have intended: that an officeholder could simply avoid future disqualification by resigning moments before the vote to convict is held. Under this view, an impeached president whose conviction was imminent and certain could simply burst in through the wall of the Senate chamber, like the Kool-Aid Man, minutes before the vote of conviction, only instead of yelling “OH YEAHHH!” the president would yell “I RESIGN! OH YEAHHH!” And unlike Michael Scott “declaring” bankruptcy by yelling “I DECLARE BANKRUPTCY!” at the workers in his office, the president’s resignation probably could take effect that quickly. I don’t think the Founders meant to allow a president to escape disqualification so easily.