It's been a couple of years since I last voted in NZ (election in 3 weeks, and it's every 3 years) but I definitely don't think you're allowed to put any identifying mark on your ballot here..
After you fill out your ballot (with no identifying marks), you slip it into an inner envelope (with no identifying marks) and put that in the outer envelope (which includes your name and you have to sign).
When a ballot is received, elections officials check the signature on the outer envelope. If the signature matches, the inner envelope containing the ballot is removed from the outer envelope and dumped into a pile so no one can match the submitted ballot with the original envelope, and then the whole pile is taken in to be counted. There's an observation deck in the facility and cameras running the entire time the elections officials are counting ballots to make sure no one is cheating and checking who voted for who.
People trust things they understand. Counting votes manually is easy to understand. It's hard to trust an electronic system.
It's trivial to tamper with such machines.