I want OnClick to fire the same frame that the button is clicked

I made a pause button that then pauses the game by setting Time.timescale = 0. I use the editors On Click {} event. The code looks like this:

public class PauseAndPlay : MonoBehaviour { public GameObject pauseButton; public GameObject playButton;

 public void Pause()
 {
     
     SaveAndLoad.saveAndLoad.Pause();
     pauseButton.SetActive(false);
     playButton.SetActive(true);

 }

 public void Play()
 {
     pauseButton.SetActive(true);
     playButton.SetActive(false);
     SaveAndLoad.saveAndLoad.Unpause();
 }

}

The problem then comes when my player continues to move for a bit even though the game has been paused with Time.timescale. I move my player like so:

//If mousepress is detected if (Input.GetMouseButton(0)) {

         //set the place as a vector
         targetPos = cam.ScreenToWorldPoint(Input.mousePosition);
         targetPos.z = 0;
         //Get screen height and width
         screenBounds = cam.ScreenToWorldPoint(new Vector3 (Screen.width, Screen.height, 0));
         //Clamp the target position so that player can't leave camera view
         targetPos.y = Mathf.Clamp(targetPos.y, (screenBounds.z - renderSizeY), (screenBounds.y-renderSizeY));
         targetPos.x = Mathf.Clamp(targetPos.x, (screenBounds.z - renderSizeX), (screenBounds.x - renderSizeX -2/*-2 because of next line where + Vector3.right * 2 */));
         //move to the place, but a bit forward so the finger doesn't obscure the sprite. ActualSpeed() is an int * Time.deltaTime
         transform.position = Vector3.MoveTowards(transform.position,targetPos + Vector3.right * 2, ActualSpeed());
     }

This happens in the Update loop. So I suspect, after a few tests, that the OnClick event doesn't happen until you stop clicking, essentially GetMouseButtonUp(0) sort of thing. With the way movement is implemented in my game I would need to pause it on the GetMouseButtonDown(0) instead. Anyone know how this can be achieved?