Although the Y33 wiring shown below isn't exactly the same as your G50, the Ignition Relay (highlighted n pink) is one possible culprit.
Everything shown below and to the right of the relay contacts is switched through it, everything below and to the left of it is connected directly to the battery.
Sometimes, when the relay contacts are pitted and/or dirty, they only pass current when a substantial load is turned on. Essentially, the extra current cleans the contacts little bit, temporarily making them more conductive.
As soon as the car is turned off, the contacts open, and this better path for current flow is lost.