Unity3D_2019: Adding EventTriggers at runtime

First of all:

You will not see the added listeners in the Inspector!

In the Inspector you only see the permanent listeners, not the ones added on runtime! These are basically UnityEvent<BaseEventData>'s so see Manual: UnityEvents

When a UnityEvent is added to a MonoBehaviour it appears in the Inspector and persistent callbacks can be added.

The only way to add permanent listeners is either via the Inspector or a custom EditorScript! But this is not what you want to do here anyway.

I would slightly modify your script to make it more secure. I simply log some messages for the methods when they get called to show that they get called.

public class Example : MonoBehaviour
{
    // Rather make these directly of type EventTrigger
    // So you don't have to use GetComponent later and can be sure that these array only receives
    // objects that actually have that Component attached!
    public EventTrigger[] slots;

    private void Start()
    {
        // Instead of a hardcoded index either iterate using slots.Length
        // or simply directly foreach
        foreach (var slot in slots)
        {
            var pDown = new EventTrigger.Entry
            {
                eventID = EventTriggerType.PointerDown
            };

            pDown.callback.AddListener(eventData => { InventorySlotCopy(); });
            slot.triggers.Add(pDown);

            var pUp = new EventTrigger.Entry
            {
                eventID = EventTriggerType.PointerUp
            };

            pUp.callback.AddListener(eventData => { InventorySlotInsert(); });
            slot.triggers.Add(pUp);
        }
    }

    private void InventorySlotCopy()
    {
        Debug.Log(nameof(InventorySlotCopy));
    }

    private void InventorySlotInsert()
    {
        Debug.Log(nameof(InventorySlotInsert));
    }
}

The rest depends on your setup. We don't know what objects your slots are but there are basically two(three) options:

Option 1 - UI

If these slot objects are UI elements in a Canvas such as Image or Text.

This seems to be the case for your specifically.

1. Make sure that there is an EventSystem present in the scene.

   Usually one gets created when creating the first Canvas.

   If not create it now via Hierachy View → right click → UI → EventSystem

2. Make sure you have the option RayCast Target enabled on your slot's UI Components.

Result:

Options 2 - 3D Objects (Option 3 - 3D Objects with 2D Colliders)

Just adding this for other users.

If these objects are not UI elements but rather 3D objects make sure

1. Again you need the EventSystem as before

2. The slots have Collider Components attached to the same GameObject the EvenTrigger Component is attached to or any of its children (it may be nested).

3. Your Camera needs the Component PhysicsRaycaster attached. Make sure here that the eventMask includes the layer(s) your slot objects are placed on. (For Option 3 using 2D Colliders instead use the Physics2DRaycaster)

Result:

As you can see the methods will not be visible in the Inspector (due to the reason mentioned before) but the added listener methods still get called.