Raycast not working in 2D game

As far as I can tell, the site ate my question the last time I typed it in. Sorry if this is a duplicate.

I'm a Unity and C# noob, and have a little experience making games. I'm trying to make a Strategy RPG similar to Fire Emblem. Characters take turns moving around on a square grid. I'm having trouble getting character movement to work. I'm using a sprite to highlight movement range. It shows up at z=1 under a character, when the player clicks on that character. When the player clicks somewhere else after selecting the character, the game uses a raycast from the cursor's (x,y) coordinates through z=1 to make sure the space to move the character to is within the movement range. However, the raycast doesn't seem to be working. I've been staring at it for a while and have no clue what's wrong. I would appreciate it if someone could help me out.

Player: using System.Collections;

 public class PlayerUnit : MonoBehaviour {
 
     bool Selected;
     Vector3 CursorPosition;
     int ClickTimer;
 
     void Start () {
         Selected = false;
 
     }
     
     // Update is called once per frame
     void Update () {
         if (ClickTimer >= 1) {
             ClickTimer = ClickTimer - 1;
         }
         if (ClickTimer == 0) {
             //Select unit and display movement range.
             if (Input.GetMouseButtonDown (0)) {
                 CursorPosition = GameObject.FindWithTag ("Cursor").transform.position;
                 if (Selected == false) {
                     if ((transform.position.x == CursorPosition.x) && transform.position.y == CursorPosition.y) {
                         float XCenter = transform.position.x + 0.5f;
                         float YCenter = transform.position.y + 0.5f;
                         Object.Instantiate (Resources.Load ("PlayerHighlight"), (new Vector3 (XCenter, YCenter, 1)), Quaternion.identity);
                         Selected = true;
                         ClickTimer = 30;
                     }
                 }
             }
         }
         if (ClickTimer == 0) {
             //Move selected unit.
             if (Input.GetMouseButtonDown (0)) {
                 if (Selected == true) {
                     if (Physics.Raycast ((new Vector3 (CursorPosition.x, CursorPosition.y, 1.5f)), Vector3.back, 1f)) {
                         Debug.Log ("Raycast hit something.");
                         transform.position = new Vector3 (CursorPosition.x, CursorPosition.y, 2);
                         Selected = false;
                         ClickTimer = 30;
                     }
                 }
             }
         }
     }
 }

Highlight sprite code (only affects color): using UnityEngine; using System.Collections;

 public class MakeTransparent : MonoBehaviour {
 
     // Use this for initialization
     void Start () {
         GetComponent<SpriteRenderer> ().color = new Vector4 (0f, 0f, 1f, .5f);
 
     }
     
     // Update is called once per frame
     void Update () {
     
     }
 }
 

Cursor:

 using UnityEngine;
 using System.Collections;
 
 public class CursorController : MonoBehaviour {
     Vector2 CursorPosition;
     float CursorPositionX;
     int RoundedCursorPositionX;
     float CursorPositionY;
     int RoundedCursorPositionY;
 
     // Update is called once per frame
     void Update () {
         CursorPosition = Camera.main.ScreenToWorldPoint (Input.mousePosition);
         CursorPositionX = CursorPosition.x;
         RoundedCursorPositionX = Mathf.FloorToInt (CursorPositionX);
         CursorPositionY = CursorPosition.y;
         RoundedCursorPositionY = Mathf.FloorToInt (CursorPositionY);
         transform.position = new Vector3 (RoundedCursorPositionX, RoundedCursorPositionY, 3);
     }
 }
 

Thank you!