johnlysk:
Yes, the 2012 Blue Ox baseplate fits the 2013 MINI Cooper S Hatchback just fine. The Blue Ox part number for the 2007 thru 2013 MINI Cooper S base plate is BX1307. I also had the Blue Ox wiring kit installed which installs separate tail/turn/stop bulbs in the tail light housings. I don't recall the part number for the wiring kit, but it is on the Blue Ox web site.
Towing the manual tranny MINI is a breeze. The MINI has no steering lock so you can keep the key in your pocket.
If you want I will take a picture of the install which looks nice. Without the tow bar connectors plugged in, the base plate install is not noticeable at all.
Good luck and enjoy your MINI--Motor On!
Dean L
2004 Winnebago Journey 39W
2013 MINI Cooper S Hatchback