Just my two cents, Clemens. Without a key, I can at least switch on the parking lights on my 4/4 and see whether they are on or not.
Is there any power consumer (e.g. parking lights) on the Plus Four to see if the battery is still supplying power without the need of ignition or if it is dead as a doornail? If the battery has a short circuit, not even a consumer like the parking light would come on.