Just looked at my extra locks. They are actually from Sugatsune PKL-08 GA. But I have also seen Nakamichi locks that not only lock on push but also turn to open when out.
Look them up on the internet.
The locks have an out side and inside part. You need to drill with a core saw for the outside part. Position it well so that the inside part hooks behind the wood frame. I had to do several cut outs into the frame to close and open correctly.