A lot of redundant and overcomplicated code has been posted in this thread for what is actually a pretty simple problem. Here's a generalized simple solution that doesn't use any additional nodes and will report double tap on any key:

const DOUBLETAP_DELAY = .25
var doubletap_time = DOUBLETAP_DELAY
var last_keycode = 0

func _process(delta):
	doubletap_time -= delta
	
func _input(event):
	if event is InputEventKey and event.is_pressed():
		if last_keycode == event.keycode and doubletap_time >= 0: 
			print("DOUBLETAP: ", String.chr(event.keycode))
			last_keycode = 0
		else:
			last_keycode = event.keycode
		doubletap_time = DOUBLETAP_DELAY

It can also be easily adapted to work with actions instead of keycodes.