What other functions/options are available and attached to the red button or attached to whatever is under the cursor? I currently don't have BTT installed so can't check, and perhaps there's a way to achieve it that's not immediately obvious.
Not heard of either, but I'm assuming these run in the background and listen for messages sent by the system whenever an instance of a window is destroyed. That's something one can create themselves, in the form of a stay open AppleScript application. It would operate under the same principle (and not in a stupid that uses repeat loops or polling), by listening to system messages, so it would have to remain running. It's not going to be as efficient as an application written in Swift or Objective-C, but since loads of stuff now is written with JavaScript frameworks that rape your system for all their memory, it'll probably appear reasonably modest, save for any memory leaks which one has no control over with AppleScript (if this occurs, it means you'd need to restart the application whenever it becomes less responsive). It would also be hanging around on the dock, which might or might be annoying.