He ain’t on active duty, he voted later in the day. He was probably picking out furniture for his new office.
The thing that average American doesn't seem to grasp is that the House and the Senate have completely different roles in the impeachment process. RATs will say stuff like "Clinton wasn't fully impeached because the Senate voted against it". It doesn't work that way, impeachment isn't a piece of legislation. When there's a problem with federal official, only the House has the power to impeach them, which means they examine the situation and determine whether is suffice evidence to accuse the federal official of wrongdoing. After the official is impeached by the House, only the Senate has the power to determine the guilt or innocence of the person the House accused, by conducting a trial, calling witnesses, etc. That's why it's only a simple majority to impeach but a 2/3rds majority to convict.
So, Kirk as a Congressman concluded that there's sufficient evidence this judge may have committed a serious offense. Then, as a Senator, he would sit as a juror and hear the argument's in the judge's defense that he did not commit serious crimes, and hear arguments that the judge did commit crimes that warrant removal from office. Where's the conflict of interest? Kirk doesn't know this guy personally or stand to gain or lose if the judge is removed. As a Senator, he would be scrutinizing the judge's record far more than he did as a Congressman, where he was only looking if there was enough questionable things on the judge's record to conclude he MIGHT have committed a serious offense while in office.
Had Kirk been on the judiciary committee like Chuckie Schumer, helped drafted the articles of impeachment, served as a House manager against the judge, or testified for or against impeachment as an expert witness, you might make a decent case that his mind is already made up and it's best he sit out the impeachment trial. But as an ordinary Congressman who concludes the judge MIGHT have committed a crime and the Senate needs to have a trial on the matter, no way. He could still serve as a juror in the Senate.
Looks like Mark Kirk "the lame duck killer" is once again ignoring the wishes of his constituents and giving the RATs cover. And now Illinois sole vote in the Senate is get this judge get away his crimes, thanks to Dick Durbin's Not Gulity vote. Is that the will of the electorate electorate? I doubt it.