The below program shows a transparent (opacity = 0) rectangle and a circle inside it. Rectangle and Circle are part of a group present in a transparent stage. Mouse entered and exited events are not triggered correctly for the group - they are not consistently triggered.

import javafx.scene.*;
import javafx.stage.*;
import javafx.scene.shape.*;
import javafx.scene.paint.*;
import javafx.scene.input.*;
import java.lang.System;

Stage {
    style: StageStyle.TRANSPARENT
    width: 500
    height: 500
    scene: Scene {
        fill: null
        content: Group {
            onMouseEntered: function(e: MouseEvent) {
                System.out.println("Group mouseEntered");
            }
            onMouseExited: function(e: MouseEvent) {
                System.out.println("Group mouseExited");
            }
            content: [Rectangle {
                opacity: 0
                width: 300
                height: 300
                x: 100
                y: 100
            }, Circle {
                radius: 50
                centerX: 250
                centerY: 250
                fill: Color.BLUE
            }]
        }
    }
}