Is it possible to listen to when the animation ends and start the timer then? The current way isn't compatible with cases where this happens halfway during the transition or simulation-based transition where there isn't a predefined duration.

Yaa, was thinking the same. but for some reason below written code doesn't fix the issue.

if (route?.secondaryAnimation != null && route!.secondaryAnimation!.isAnimating) {
   _timer?.cancel();
   void onAnimationDismiss(AnimationStatus status) {
        if (status == AnimationStatus.dismissed) {
           route.secondaryAnimation!.removeStatusListener(onAnimationDismiss);
           show();
       }
   }

    route.secondaryAnimation!.addStatusListener(onAnimationDismiss);
    return;
}

In some cases the secondaryAnimation is swapped for a different one, so that may be why. The secondaryAnimation with the status listener is replaced.

Rather than putting the logic here, should we have the check happen in tandem with the _visible check for _ExclusiveMouseRegion? So it ignores all mouse events while the route transitions are in motion?

Oh yes, that will be better place and we don't even need listener.

Pushed the change, everything looks good. Thanks.

Extreme nit, for this case I think it needs a link to the issue it is checking against.

Thanks for suggestion. Pushed the change.