For those kind of things may be better to avoid background process, just use a regular processed element (on game idle update time, process in Godot).
You can have a scheduler node/scene, part of the main scene or an autoloaded one, it can make anything using timers or whatever you need.
Games like fallout use some kind of turn based system (you can see how the daylight changes, also the game time of day), it is used to define when events trigger in base of some established rules and a schedule (like when quests starts and ends).