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.