To be clear, I am only advocating a secret ballot in the US Senate impeachment trial.
Notably, Americans have always considered the secrecy of their own individual ballots is sacrosanct.
There are only 3 Democratic senators who might vote to acquit -- Sens. Joe Manchin of West Virginia, Kyrsten Sinema of Arizona and Doug Jones of Alabama -- and they have been predictably undecided from the beginning of the impeachment process.
In addition to these three, please name "the many other instances of discontent." I say you can't name one. (Nor is it certain that Manchin, Sinema and Jones will all vote to acquit.
On the other hand, Arizona's recently retired Republican Senator "Jeff Flake says 35 (thirty five) Senate Republicans would vote to convict Trump if impeachment featured a secret ballot"
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
If Republican Senator Flake is even remotely close to right -- and even if all 3 Democratic senators defect -- a secret ballot would result in Trump's ouster by a landslide.
To be precise...
If Manchin, Sinema and Jones all vote to acquit, the Democratic caucus still has 44 votes (including two Independents).
Add 23 of Flake's 35 senators to the 44 Democratic caucus votes and Trump is outta here.
Concerning your desire "to identify who votes in which direction" for purposes of future political orientation, that is your desire, but open (non-secret) voting in Senate impeachment trials is not obligated by constitutional law.
I, on the other hand, desire to have senators vote their conscience in this unique circumstance of a Senate impeachment trial.
Therefore, I advocate that senators be liberated to vote their conscience through secret balloting.