[silverfox666]

Update on this - for anyone who experiences a similar sound...

After taking the whole centre console 'out' I managed to find that it was the Z shaped bracket that bolts to the floor that was transferring the vibrations from the car up into the gear lever module. Then it was buzzing...

I had to take several layers of parts out to get to it and then you are faced with 4 bolts. Two are plastic and will shear really easy and the other two are locking nuts. I loosened them all and removed the plastic ones (to break the transfer of vibration). This appears to have worked. I am mindful of the Z bracket now not being secured in, but it's properly 'trapped' so can't move anyway.

This problem almost made me give the car back as it was a joke and the dealership couldn't hear it... whenever I took it in (typical!)

One thing I will say is that I am pleased BMW chose to use mainly T20 screws for everything - makes it simple to take apart!

I've attached a diagram to show where the part is (and I think this isn't an F10 LCI centre console, but it's similar), it was part '6'

Hope this helps someone somewhere!