Yes, the Constitution requires the state include a list of what candidates received votes from the state. Which would preclude secret ballot.
But some states have secret ballot, which are then counted that same day by the state. So it wouldn’t be clear who the faithless Elector is.
Besides Washington state, there were 4 other faithless votes sent to Congress. Congress counted them.
"Secret" meaning who casted the vote, not for whom they voted.
-PJ