Will the vote to approve a secret vote be secret?
I’m not even sure the Senate can have secret votes of any kind. If you don’t record each person’s vote how can the result be official?
Elections are by secret ballot. Votes in Congress are different.
Will the vote to approve a secret vote be kept secret?
Long enough for the actual vote to be taken if it passes. Then the Democrats will leak both votes so the outrage will sink the re-election of every Senator who voted for conviction and removal from Office and likely disqualification from holding further Office to prevent his re-election. Republicans have so many up for re-election next year that the Democrats would end up with a veto proof majority and the Democrats would have free reign control of the Government no matter who gets elected President.