I could not detect any significant discharge during storage. Therefore, it is probably not necessary to charge the booster constantly.

Sockets in the boot normally switch off when the key is out of the lock. At least in more modern cars.

But I can't recommend the GB70. With a 3L diesel with a flat battery, it's not even enough for preheating. With petrol cars you'll get far, the GB150 will still start a car where the battery is really flat. With diesels with a completely dead battery, however, it also reaches its limit.