Eye Follow Mechanics on Light

I'm currently trying to get similar mechanics to an eye following the mouse, but the only moving part is a light (there is no eyeball)

I'm having two issues, and they are:

1. The light moves from it's position to the centre of the screen

2. The light moves away from the mouse as opposed to towards

Here is my code

 public float m_EyeRadius = 100.0f;

 private Vector3 distanceToTarget_;
 private Vector3 finalPos_;
 
 void Update () 
 {
     distanceToTarget_ = Camera.main.ScreenToWorldPoint(new Vector3(Input.mousePosition.x, Input.mousePosition.y, transform.position.z)) - transform.position;
     distanceToTarget_ = Vector3.ClampMagnitude(distanceToTarget_, m_EyeRadius);

     finalPos_ = transform.position + distanceToTarget_;
     transform.position = new Vector3(finalPos_.x, finalPos_.y, transform.position.z);
 }

Perhaps someone else can see where I'm going wrong in this, but I'm drawing a blank at the moment. This script (and this is the entire thing) is attached to the light.