C# How to remap a key click (left-right) to a touch on an object on the screen (for example, a left-right arrow)?

Question

C++ / C#

Script for the character, namely - the part related to movement

public class MovePlayer : Unit

private void Update() 
    {
        if (Input.GetButton("Horizontal")) Run();
    }

private void Run() // 
    {
        Vector3 direction = transform.right * Input.GetAxis("Horizontal"); 

        transform.position = Vector3.MoveTowards(transform.position, transform.position + direction, speed * Time.deltaTime); 

        sprite.flipX = direction.x < 0f; 
    }

Script for Arrows. The click check works, it remains to somehow connect it with the Run method or even enter the object into the script for the character ...

public class Touch : MonoBehaviour
{
    void Start()
    { 
 
    }
    
    void OnMouseDown()
    {
        Debug.Log("OnMouseDown");
      }
}