Interesting, thanks for the tip. However I am a bit confused about the concept of an 'amplified' aerial. The shark fin I am looking at is an amplified aerial, with a standard male DIN plug and a 12v wire. Am I right in thinking that the amplification electronics are in the base, powered by the 12v feed? In which case if I used the adaptor you have shown would not still not get an amplified signal? I had come across the 'FAKRA' connectors whilst googling this problem but couldn't be sure that this was the right female connector for the plug on the cable. It did ocurr to me that after all this faffing about the signal would probably turn out to be rubbish!
Sorry, didn't realise the sharks fin aerial was amplified so if you connect the 12V to the original switched 12V it will act the same as the aerial you are replacing.
However, In my opinion the antenna design is still compromised compared to a traditional whip design so the amplifier doesn't really add much in that the story goes 'Garbage in, Garbage out', in other words, poor quality low power signal input to an amplifier is still a poor quality signal when you amplify it because you can't replace what was never received....