Here's where it gets tricky; where the ideals of the Founders clash with the realities of our foibles, especially pronounced at this time. Black writes:
The Constitution says, in Article III (the Judiciary Article), that “the trial of all Crimes, except in Cases of Impeachment, shall be by Jury . . .”; the implication is that the impeachment trial is a “trial” much like others, except that a jury is not to be used. The special oath which senators take has already been mentioned. The Senate is to “try” all impeachments, not simply vote on them; the word “try” is a word used almost invariably in regard to judicial trials. Political good sense points the same way; a judicial or quasi-judicial trial is simply one that inquires into the facts and the law, without partisan or narrow political bias, and proceeds to judgment accordingly—these things are obviously what we want in impeachment proceedings. In function, then, the “trial” in the Senate is, as its name implies, at least quasi-judicial. The important thing is not the name given but the thing desired—total impartiality, at least resembling that of a faithful judge or juror.
Here a difficulty arises—one which can be solved only by great and self-insightful integrity. It must almost always be the case that many senators find themselves either definitely friendly or definitely inimical to the president. In an ordinary judicial trial, persons in such a position would of course be disqualified to act, whether as judges or as jurors. It cannot have been the intention of the Framers that this rule apply in impeachments, for its application would be absurd; a great many senators would inevitably be disqualified by it, and it might easily happen that trial would be by a quite small remnant of the Senate. The remedy has to be in the conscience of each senator, who ought to realize the danger and try as far as possible to divest himself of all prejudice. I see no reason why this cannot produce a satisfactory result. [Emphasis added.]
Black, Charles L., Jr. & Bobbitt, Philip, Impeachment: A Handbook, New Edition (pp. 11-12). Yale University Press. Kindle Edition.