A standard 12v auto socket is too large to fit in the socket fitting under the tank. Auto 12v sockets also do not generally have a locking device to keep the plug attached. The result is that after a bit of vibration, the plug tends to back out. Look for a BMW plug.
If you intend to mount it on the bar and don't mind the plug vibrating out every now and again, it's no big deal.
You can find plugs at
Rider Warehouse