Do I get 12V on OBDII pin 16 without ignition ON?
Not a good idea - leave the OBD connectors for OBD. Instead, a simpler solution is to look for an add-a-circuit device in your local car spares store. Plug it into a known 12V supply in the cars cabin fusebox, and run the power lead to the dashcam.
This is a much quicker solution than trying to find switched 12V in the OBD connector, and is completely reversible if you want to remove the dashcam when you sell the car.