Tiguan fast rattle / vibration when towing

I tow with a 2012 Tiguan with a Brink retractable towbar. Owned for 8 months. Only when towing do I get an annoying fast rattle, like a noisy vibration, at the rear of the car. I just cannot track it down, having tried everything I can think of. I tow a trailer as well, and then there is no rattle. So I reckon the fairly substantial noseweight is the cause. The weird thing is I lived with exactly the same rattle for 5 years in my earlier 2008 Tiguan and identical towbar! Has anyone else had the same problem and more usefully, has it been solved?