I don’t believe I have ever declared a party and I have voted for years and years.
Always printed out name and signed a paper. Paper was compared to voting roll, name was crossed off and I was given a ballot. I don’t recall if it was numbered or not but I usually ask how many have voted.
We still have, or at least we had in 2010, the same system. The ballot was via black pen connect-the-arrow method then I put the ballot in an automated tabulation thingy and my ballot was put in a locked cylinder.
Oh, and we do have to show ID.