From the bottom of page 178 of the document you linked:

VII. The Presiding Officer of the Senate shall direct all necessary preparations in the Senate Chamber, and the Presiding Officer on the trial shall direct all the forms of proceedings while the Senate is sitting for the purpose of trying an impeachment, and all forms during the trial not otherwise specially provided for. And the Presiding Officer on the trial may rule on all questions of evidence including, but not limited to, questions of relevancy, materiality, and redundancy of evidence and incidental questions, which ruling shall stand as the judgment of the Senate, unless some Member of the Senate shall ask that a formal vote be taken thereon, in which case it shall be submitted to the Senate for decision without debate; or he may at his option, in the first instance, submit any such question to a vote of the Members of the Senate. Upon all such questions the vote shall be taken in accordance with the Standing Rules of the Senate.

The Presiding Officer of the Senate is Mike Pence, so he basically has complete control over every aspect of the trial, meaning McConnell has complete control because Pence is as much his bitch as every other Republican is.