61 13... Circular connector, 13-pin, system D2.5
WARNING: This page is about a different car, the 2013 BMW 550i GT, 2012 BMW 550i GT, 2011 BMW 550i GT, and 2010 BMW 550i GT. However, it is still accessible from the selected car via links, so may be relevant.
Special tools required:
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.