I believe there is a way to have the object itself handle the input. I've not done this ind 3d but I have in 2d. You need to set the object up to handle unprocessed input. This just means that any click events or press events that no other object has 'consumed' will fire off events.
When you are in your _unhandled_input event you decide if that object wants to 'claim' the input and you mark it as such using SceneTree.set_input_as_handled(). For example if your object can be left clicked but not right clicked then you would set_input_as_handled for left clicks but not right. So that means that left clicks will stop at your object but if you right click it, then anything behind it will get a chance to handle the right click.
Think of an input event as happening along a line in your 3d world. It goes through all the objects that are on the screen starting with the one that is in the foreground and moving back.
Take a look here:
http://docs.godotengine.org/en/stable/tutorials/engine/inputevent.html