So this is an APB out to anyone with this un welcomed issue with their Aux port side of the 2014 Countryman S audio access located at the base of the center console where the gear shift **** sits. My port had a 3.5 input connector somehow break inside the Aux port, so my music or any type of Bluetooth accessible device was useless, I thought and burned brain cells on how to get the broken piece out for quite a few days, I thought of toothpicks with glue at the tip to try to adhere to it and dislodge and pull it out, I then continued looking through my tool case and found some very small screw drivers that I had for a past phone repair, so I attempted to use em’ with no luck, I then turned to my wife and asked her to help me, it was hot outside this Central FL, Saturday AM. She suggested a small set of pliers from our surgical job, that we had here at home, so as she tried she figured out that the plug n play USB/AUX port, could be maneuvered out from the inside of the gearbox casing, so we figured it out, a somewhat fragile plastic cosmetic ring around the shift stick popped off carefully, then the “fleather” around the actual shift **** slid upward and “Walla” the entire encasement under and behind the said port was accessible and exposed there at the center console, so easily then to just unplug the port and take the entire USB/AUX off, to carefully pry out the broken little piece out. Work in reverse and easily just plug the access port back on and place the 2 or 3 pieces back together and problem solved......
I will upload a short video later, because after checking everything back to proper operating order, I just wanted to write this out to help anyone else who encountered this same issue.No need to disassemble the entire dash and center console to work on anything, nothing major to take apart, and so much relief.....

 

Earth magnet would have been my first choice. Your idea as a backup plan.

 

I did try the magnet, the small piece gets lodge between the two prongs that secure the 3.5 port tip, it doesn’t just slide out....

 

That makes sense!