I think I know why Corker voted for it. It’s a quaint thing in the Senate rules that you essentially have one person vote against the fillibuster to retain tehir right to fillibuster.
A voice of reason. That is exactly what they do — Corker was the person for the GOP Senators.
I’ve heard of that rule before but somehow I wouldn’t be surprised to see that Corker actually supports this.
No. You are mixing up the right to reconsider the vote with the right to "unlimited debate." Scare quotes, because Senate rules don't require holding the floor in order to object to setting a time to take the vote. A senator can object to voting, without taking a vote stand one way or the other. But, in order to move to reconsider a vote, one has to be on the winning side. There is no point to a motion to reconsider a cloture vote, once cloture (a 30 hour time limit on debate) has been agreed to.
Rather, only a Senator on the prevailing side may bring it up again.