How to lock / unlock Cursor and Mouselook when using FPSController

I'm working on a Unity 5 project and am using the First Person Character prefab to handle the player character. I'm struggling to implement a pause menu because I cannot figure out how to correctly lock and unlock the cursor and mouselook.

In my current code, the cursor unlocks when the game is paused, but locks as soon as the player clicks (even if they game is still paused). It also fails to lock when the game is unpaused, again unless the player clicks. The MouseLook also never seems to disable, meaning the camera is visibly swinging around when the game is paused.

I want a way to lock the mouse look and unlock the cursor for the entire time the game is paused so that the player can interact with the menu, and do the reverse whenever the game is not paused to let the player play the game.

Here is a sample of my UI controller that is meant to handle the logic for pausing and unpausing the game:

 public class UIManager : MonoBehaviour {
     private AudioSource pauseSource;
 
     public GameObject PanelPause;
     public SettingsManager settingsManager;
     public FirstPersonController player;
     public bool isPaused = false;
 
     void Start () {
         pauseSource = GetComponent<AudioSource> ();
         
         pauseSource.ignoreListenerPause = true;
         pauseSource.Play (); 
         pauseSource.Pause ();
         
         PanelPause.SetActive(isPaused);
     }
         
     void Update () {
         if (Input.GetButtonDown("Cancel")) {
             isPaused = !isPaused;
         }
 
         if (!isPaused) {
             PanelControls.SetActive(viewControls);
         }
 
         setPause(isPaused);
     }
 
         public void setPause(bool pauseState) {
             player.m_MouseLook.SetCursorLock(!pauseState);
 
             PanelPause.SetActive(pauseState);
             AudioListener.pause = pauseState;
 
             if (pauseState) {
                 // Do logic to pause
                 Time.timeScale = 0.0f;
 
                 pauseSource.Pause();
 
                 Cursor.lockState = CursorLockMode.None;
             } else {
                 // Do logic to unpause
                 Time.timeScale = 1.0f;
 
                 pauseSource.UnPause();
 
                 settingsManager.exitSettings();
 
                 Cursor.lockState = CursorLockMode.Locked;
             }
     }