Double tap, Longpress
unfortunately these concepts do not exist in InputEvent
There is an option in project settings that lets you emulate ScreenTouch as mouse events, you'll be wanting to enable that.
The preferably have an autoload to pool unhandled events
func _unhandled_input(event):
var new_event
if event is InputEventScreenTouch:
if event.pressed:
new_event = InputEventMouseMotion.new()
new_event.position = event.position
Input.parse_event(new_event)
As mentioned before the other conditions do not exist and you will have to code it on your lonesome