61 13... Circular connector, 13-pin, system D2.5
WARNING: This page is about a different car, the 2010 MINI Cooper and 2009 MINI Cooper. However, it is still accessible from the selected car via links, so may be relevant.
Pull off rubber grommet (1).
Carefully pull out lock (2) in direction of arrow.
Move lower section of connector (3) in direction of arrow until retaining lugs (4) snap into release groove (5).
With special tool 61 0 303 , press down retaining lugs (6) of corresponding contact and pull out cable.