You'll want to use input events, since those just fire once when you press the key. Then you just set a timer for whatever double-tap speed you want, and if it's still playing when you press the same key again, that's your double-tap.
func _input(event):
if event.is_action_pressed("left"):
if get_node("Timer").is_processing():
double_tap_left()
else: get_node("Timer").start()
