Republican Senator Jeff Flake has stated that if the senate vote to remove Trump based on this week’s findings were done by secret ballot, at least 35 of the 52 republican senators would vote to remove Trump.
https://www.marketwatch.com/story/jeff-flake-says-35-senate-republicans-would-vote-to-convict-trump-if-impeachment-featured-a-secret-ballot-2019-09-27
The implication here is that at least 35 republican senators will not vote in the way they feel would be in the country’s best interest, due to political worries.
Here is an article from 1999! arguing that the Senate both has the legal right to vote to remove the president by secret ballot, and the constitutional duty to do so…
https://www.thecrimson.com/article/1999/2/5/the-senate-should-vote-in-secret/
"The Constitution makes clear that the Senate may convict an impeached president with the "concurrence of two-thirds of the Members present." But it is silent as to the exact procedure that the Senate should follow at the trial's end to determine whether two-thirds concur.”
The senate has the full authority to pass a rule by simple majority vote stating that this vote be held by secret ballot.
The article argues that the impeachment process is a trial and that the Senate acts as the Jury in order to find the president guilty and the constitution specifically states that all Jury votes must be done in secret.
The reason why the Constitution states that Jury votes must be done in secret, is the founders knew that personal considerations (such as fear of safety of person or of their office/livelihood) can override the jury’s desire to vote their conscience and to vote the way they feel is correct.
The Jury in any trail is far better informed of the evidence of guilt than the general population. They are exposed to information that is kept from public view due to privacy concerns. And the constitution states that the Jury vote be done by secret ballot, in order to ensure that these well informed Jurors are encouraged to vote their conscience, free of external influences.
Removal by Congress is one of the only remaining checks on the executive branch. The presidency has dramatically expanded its power over the past 200 years. If political concerns deter the senate from removing an executive that is so flagrantly violating the constitution that even the majority of his own party feel that he is violating the constitution, then it is in the nation’s best interest to allow the senate to vote by Secret ballot.
This vote will set a clear precedent. Is the office of the President, constitutionally allowed to use their executive influence to get other government officials to investigate their political challenger? Can the justice department (Barr) be asked by the President to get a foreign investigation opened into a political rival. If the Senate finds that the President doing this is not guilty of a constitutional violation, then every future executive has free reign to use their influence to get their political opponent’s investigated.
In the two party system, without a secret ballot, would the majority of a party’s senators EVER vote against the party leader no matter how flagrantly they violate the constitution? No, not with the divisive partisan system we employ. This is why a secret ballot is neccesary, because it is the only situation in which congress would ever exercise it’s constitutional duty to remove an out of control, and constitutionally reckless executive.
If Trump fans are so adamant that he did nothing wrong, they should expect that a secret vote on his guilt would find the overwhelming majority of the entire senate to vote to not find him guilty, a vote so in favor of Trump that it would serve as a giant F U to people that felt he should be removed from office.
The only situation in which not even a third of the senate would vote to keep Trump in power, is if Trump really is so recklessly violating the constitution that 35 republican senators would vote against him as well, if they could vote their conscience.