interesting takethere is no rule or oath that a senator must remain impartial ...impeachment is a political process and has nothing to do with fairness...any member of the senate can call for a dismissal at any point in the trial and effectively end it before it begins with a simple majority vote to aquit...even if justice roberts refuses to dismiss he can be overruled by the senate simple majority...the rules of the senate are exclusively for senators and may be changed and or modified even at mid trial....and nothing is official till it is recorded by the secretary of state after the trial ends
here's what i read, seems a little at odds with your statement
The Constitution requires senators to take a special oath or affirmation to participate in impeachment proceedings. It doesn’t specify what the oath must say, though the chamber’s practice has been to require each senator to promise “impartial justice.”
The wording of the oath was established in the first impeachment proceedings, the 1798 trial of Senator William Blount: “I, (name) solemnly swear, (or affirm, as the case may be,) that in all things appertaining to the trial of the impeachment of (name), I will do impartial justice, according to law.”