If the ballot is secret and the Elector who voted is not known,
That’s an ‘if’ which doesn’t exist. The votes are open and known when they occur.
Are Electors’ ballots public information? I don’t think so.
They are. That’s part of how we know which Elector voted in peculiar ways.
Article I says that Congress must record the yeas and nays, but it says nothing about the Electoral College.
The Electoral College is a vote in each individual state, which is then sent to Congress - and then validated by Congress. From time to time, Congress has invalidated submissions by states, such as one incident where two sets of results were sent.
The 12th amendment says they vote by ballot, not recorded yays and nays. In this country, ballots have always been secret.
-PJ