How does headwind influence the results of a pitot tube and therefore the airspeed indicator? What I know so far

I recently read about pitot tubes and their use in aircraft. For the basics I consulted Wikipedia, and also went through the definitions for airspeed, groundspeed, and the various other airspeed definitions (TAS, IAS, EAS, CAS). Furthermore I made myself familiar with aircraft speed indicators.

At first everything seemed logical, I thought I understood the working principle. But then a few days ago I came across the question how wind (headwind, for that matter) is accounted for on the airspeed indicator.

Question

Assume an aircraft that is standing still on the ground, experiencing a 60 kt headwind. Will the airspeed indicator show anything that is related to that headwind? Why/why not?
The pitot-static system (and the airspeed indicator) doesn't care about the speed of the aircraft with respect to the ground. It is concerned only with the speed of air with respect to the aircraft (that is why it is called airspeed and not groundspeed indicator).

So, if your aircraft is on ground and experiences a headwind of 60 kt, the airspeed indicator will show an airspeed of 60 kt, in an ideal case.

This is important because the wing generates lift depending on the airspeed, not the ground speed (forgetting about stuff like ground effect, etc.). This means that if an aircraft is parked on the ground and there is a headwind of sufficient velocity, it will try to lift the aircraft up.