How to move forward after staring at one point then stop when looking elsewhere ?

Note: This is untested code, you can use this as a base to refine your own perfect movement system:

 using UnityEngine;
 using System.Collections;
 
 public class PlayerMovement : MonoBehaviour {
 
     public float maxRayDistance = 100f;
     public float waitTime = 2f;
     public float headMovementRange = 3f;
     public LayerMask layerMask;
     private bool waiting = false;
     private Vector3 currentRayPosition;
     private Vector3 initialRayPosition;
     public Transform player;
     private RaycastHit target;
 
     private void MoveToTargetPos(Vector3 position)
     {    
         player.transform.position = initialRayPosition;
     }
     
     private IEnumerator WaitForMovement()
     {
         yield return new WaitForSeconds(waitTime);
         MoveToTargetPos(initialRayPosition);
         waiting = false;
     }
     
     // Update is called once per frame
     void Update () {
         
         Vector3 rayDirection = transform.TransformDirection(Vector3.forward);
         Ray ray = new Ray(transform.position, rayDirection);
 
         // Fire a ray from current head position towards rayDirection with a range of maxRayDistance
         if (Physics.Raycast(ray, out target, maxRayDistance, layerMask))
         {
             if(!waiting)
             {
                 // This is the first time the ray hits the ground, so let's store that position
                 initialRayPosition = target.point;
                 StartCoroutine(WaitForMovement());
 
                 // Set waiting to true so we start the coroutine only once
                 waiting = true;
             }
             
             // Store the current position of the ray
             currentRayPosition = target.point;
             // Calculate distance between the first ray and the current ray
             if(Vector3.Distance(initialRayPosition, currentRayPosition) > headMovementRange)
             {
                 /* 
                     The distance is larger then headMovementRange, so stop the coroutine and let's start
                     from the beginning
                 */
                 StopCoroutine(WaitForMovement());
                 waiting = false;
             }
         }
     }
 }
 

Attach this script to your eye camera and assign the player transform reference and test it out. Basically what it does:

It fires a raycast forwards from the head position and stores the point it hits the ground. Then it starts a timer that waits for the time specified with waitTime The update loop continues to fire rays and calculates the distance between the first ray that hit the ground and the ray that is currently hitting the ground. If the distance exceeds headMovementRange, we start this process from the beginning.