What you'll want to do is have, like you said, a node implement _unhandled_input and then call set_process_unhandled_input(true).
Example Code:
extends Node2D
func _ready():
set_process_unhandled_input(true)
func _unhandled_input(event):
if event.type == InputEvent.MOUSE_BUTTON:
print("Unhandled Mouse Button Down or Up Event")
