Unity jagged mouse input detection

I wrote a script that writes Input.mousePosition into a file on every frame. The idea is that I want to identify which button on screen the player is trying to click before actually clicking, from the speed of the mouse basically. However, I ran into data like this:

(1113.0, 835.0, 0.0)
(1113.0, 835.0, 0.0)
(1113.0, 835.0, 0.0)
(1126.0, 835.0, 0.0)

Basically on one frame the x position is one value, a couple of frames later it's changed, but in the middle there is no gradation. While my mouse movement was continuous, if I'm to believe Unity, in the example above I hovered on 1 pixel for 3 frames then jumped 13 pixels to the right in one frame. Why is this? Is there any code to get the actual frame by frame position of the mouse?

EDIT:

    Vector2 _lastPosition;
    StreamWriter _mouseData;

    // Start is called before the first frame update
    void Start()
        {
        _mouseData = new StreamWriter(File.Open("sdata.txt", FileMode.Create));
        }

    // Update is called once per frame
    void FixedUpdate()
        {
        _mouseData.WriteLine(Input.mousePosition.ToString());
        
        if (Input.GetMouseButtonDown(0))
            {
            _mouseData.WriteLine("CLICK\n\n");
            }

        _lastPosition = Input.mousePosition;
        }

    void OnDestroy()
        {
        _mouseData.Close();
        }

EDIT 2: I changed the code to the following:

void FixedUpdate()
        {           
        _mouseData.WriteLine(Vector2.SqrMagnitude(new Vector2(Input.GetAxis("Mouse X"), Input.GetAxis("Mouse Y"))));

        if (Input.GetMouseButtonDown(0))
            {
            _mouseData.WriteLine("CLICK\n\n");
            }
        }

Now I'm still getting output that's 50% 0-es and non-0 values are sprinkled in on every second row. Exceptions: a few rows where actual values are supposed to be still contain random 0-es. Now, I'm not super concerned about getting less frequent than 1/frame data, but there's no way to distinguish between these false 0-es and actual 0-es when the mouse is not moving, which is an issue.