How can I extend Godot's Button to distinguish left-click vs right-click events?

I created a button using the built-in Button class, and set the button mask to BUTTON_MASK_LEFT | BUTTON_MASK_RIGHT. Now both left- and right-click cause the 'pressed' signal to be emitted, but I need a way to tell whether the user clicked with the left or right mouse button.

Extend the Button class, and create and emit custom signals when the button gets left-clicked or right-clicked.

In Godot 4:

class_name EventButton
extends Button

signal left_click
signal right_click

func _ready():
    gui_input.connect(_on_Button_gui_input)

func _on_Button_gui_input(event):
    if event is InputEventMouseButton and event.pressed:
        match event.button_index:
            MOUSE_BUTTON_LEFT:
                left_click.emit()
            MOUSE_BUTTON_RIGHT:
                right_click.emit()

In Godot 3:

class_name EventButton
extends Button

signal left_click
signal right_click

func _ready():
# warning-ignore:return_value_discarded
    connect("gui_input", self, "_on_Button_gui_input")

func _on_Button_gui_input(event):
    if event is InputEventMouseButton and event.pressed:
        match event.button_index:
            BUTTON_LEFT:
                emit_signal("left_click")
            BUTTON_RIGHT:
                emit_signal("right_click")