In the latest Practical Caravan (Expert Q&A, issue 438), Dave Marshall asks if the battery is being charged when he is towing. Unfortunately, as suggested in the reply, there is no definitive answer.
Our tow cars over the past 14 years have been BMW 530D, Audi Q5, Porsche Macan S diesel and Porsche Macan S petrol. All were bought new with a factory-fitted towbar and electrics, but not one had pin 10 connected, and this is the connection that would charge the caravan battery or power the fridge.