The best way to determine if a sprite is clicked is to actually use a different node, Area2D. You will use 3 nodes: a parent Area2D node with 2 child nodes, your sprite node and a CollisionShape2D node. It should be structured like this. For the CollisionShape2D, you will have to give it a Shape2D object. I usually use a RectangleShape2D. Then, change the Shape2D object's extents to make it as big as you need, usually to match the size of your sprite (Note that your extent values should be half of your sprite's dimensions. e.g. if your sprite is 32x32, make your extents 16x16).
As for code, add a script only to Area2D and use the input_event(...) function. The code will look something like this:
func _input_event(viewport, event, shape_idx):
if event.type == InputEvent.MOUSE_BUTTON \
and event.button_index == BUTTON_LEFT \
This should get you a clickable sprite. Now, if your sprite could possibly overlap other sprites that do something when clicked, that gets a little more complicated (and interesting!). Let me know if you will need to handle this case.