Sorry I'm drawing a blank. I did spot in the 2000 Miata wiring diagram both brown/white and violet/white go to the hazard warning switch. Brown/white brings power from the "Hazard" fuse and violet/white from the "Turn" fuse, but it might be a red herring.
It's going to be pretty obvious that connection only has a male end to mate up to hence why they made the connection that shape. So if it was originally a none used connection (there can be many around the car) your problem could be a could be elsewhere, another loose or missed connection.