Accordingly to POLITICO:
But what if senators could vote on impeachment by secret ballot? If they didn’t have to face backlash from constituents or the media or the president himself, who knows how many Republican senators would vote to remove?
A secret impeachment ballot might sound crazy, but it’s actually quite possible. In fact, it would take only three senators to allow for that possibility.
Three? Really? Then why not try?
BUT DON'T "TRY" IN PRIVATE.
Imagine the impact of a publically debated decision to hold secret ballots--at least on calling witnesses. The old guard in Congress rarely recognize how times have changed. As a result, they are forever missing opportunities to make hay while the sun shines. It doesn't matter if the grass is mostly weeds. Bundle it up and sell it anyway. Someone (e.g. the press) will put it to good use.