Ah, sorry. I didn't pay enough attention to your first message.
- It'd take an entirely different system to minimize to tray instead.
If you are able to pay for that (rough estimate is $100..$150 depending on features), that could be implemented into this or a separate extension.
(if you are wondering, this extension similarly exists only because someone sponsored the development and was fine with it being made publicly available) - Conventional (DirectX) fullscreen rolls up on the monitor that it was initialized for, so usually the primary one.
It's usually possible to move the game window between screens via Win+Shift+Left/Right, but I'm not sure if you could cheat it by pressing those keys via keyboard_key_press.
If window_set_rect has any effect in fullscreen (or you are fine with borderless fullscreen), I could modify my other extension to return screen XYWH per monitor index.