61 13... Circular connector, 20-pin, system D2.5
WARNING: This page is about a different car, the 2016 MINI Cooper Paceman, 2015 MINI Cooper Paceman, 2014 MINI Cooper Paceman, and 2013 MINI Cooper. However, it is still accessible from the selected car via links, so may be relevant.
Special tools required:
Carefully press back retaining tabs (1) of internal connector (2).
Turn internal connector (2) until retaining lugs (1) snap into release groove (3).
With special tool 61 0 303 press down retaining hook (4) of corresponding contact and pull out cable.