You mean that pressing the l2 makes your gaming figure look up as the joystick would do? If so,that is a very weird issue indeed. I’d force has something to do with it,you could take it apart and put it back together to see if something had pressure on it. For looking up and down,the joysticks are usually what are used. The arrow pads are making contact with a green plastic film circuit board,that’s also used with the l2 button. But the joysticks are usually used in most games like fortnite,to move and look up or down.
Has it been dropped at all? It’s always possible the processing chip has a loose connection..
Also,each joystick has 2 Little green squares Next to it. If you pop the green square apart,you find white looking wheels inside. These are what control the electricity flow so that the controller knows which direction you’re pushing the joy stick. If one is loose,maybe it is making contact at random.
I still don’t see how pushing the l2 would cause this only when pressed harder. But I guess the processing chip could be bad and pressing the l2 is not being processed by the chip correctly and it gets mixed up thinking you’re moving the joystick.