Gamepad/Mouse Virtual Cursor

You can use the function warp_mouse either on Viewport (for a 3D game) or Control (on a 2D game or UI).

You can also use the function warp_mouse_position on Input, which will work globally. Here is an example.

extends Node2D

onready var cursor = get_node("Cursor")
var mouse_pos = Vector2()
var mouse_speed = 3.0

func _ready():
	Input.set_mouse_mode(Input.MOUSE_MODE_HIDDEN)

func _process(delta):
	var mouse_rel = Vector2.ZERO
	if Input.is_action_pressed("mouse_up"):
		mouse_rel += Vector2.UP * mouse_speed
	if Input.is_action_pressed("mouse_down"):
		mouse_rel += Vector2.DOWN * mouse_speed
	if Input.is_action_pressed("mouse_left"):
		mouse_rel += Vector2.LEFT * mouse_speed
	if Input.is_action_pressed("mouse_right"):
		mouse_rel += Vector2.RIGHT * mouse_speed
	if mouse_rel != Vector2.ZERO:
		Input.warp_mouse_position(mouse_pos + mouse_rel)
	cursor.position = get_global_mouse_position()

func _input(event):
	if event is InputEventMouseMotion:
		mouse_pos = event.position

Here the node "Cursor" is a sprite of a mouse cursor, and the input mapping for "mouse_up" is the up arrow on the keyboard, "mouse_left" is the left arrow, etc.

The script needs to be on the node above the Cursor (so Menu in this case). Then also change the top line to extends Control

Your gamepad is likely switching focus around, read up on how UI focus properly works. Nodes need to be set up with references to their 'neighbors' so that the next or previous UI element could be selected/focused on.

https://docs.godotengine.org/en/stable/tutorials/ui/gui_navigation.html

You probably need to generate a custom input event.

https://docs.godotengine.org/en/stable/tutorials/inputs/inputevent.html

I just tried my code with a button and it seems to work fine. Can you explain more about your setup?

I tried to fix it, but I don't have time tonight. The trick is to generate an input event when you press the gamepad button (not using the UI input mapping).

func _input(event):
	if event is InputEventMouseMotion:
		mouse_pos = event.position
	if event.is_action_pressed("pad_click"):
		var ev = InputEventMouseButton.new()
		ev.button_index = 0
		ev.pressed = true
		ev.global_position = get_global_mouse_position()
		Input.parse_input_event(ev)

But I couldn't get it to work, maybe I can check tomorrow or you can try to figure it out.

Make sure to do input processing in _input(): rather than _process(): unless absolutely necessary so that input events can happen and be process in between frames being rendered too.