How would I detect a right click with an event trigger?

Creta a new c# script, call RightButtonEvent and paste it:

 using UnityEngine;
 using UnityEngine.UI;
 using UnityEngine.EventSystems;
 using UnityEngine.Events;
 using System.Collections;
 [ExecuteInEditMode]
 [AddComponentMenu("Event/RightButtonEvent")]
 public class RightButtonEvent : MonoBehaviour, IPointerEnterHandler, IPointerExitHandler {
     [System.Serializable]public class RightButton : UnityEvent{}
     public RightButton onRightDown;
     public RightButton onRightUp;
     private bool isOver = false;
     void Start () {
     }
 
     void Update () {
         if (Input.GetMouseButtonDown(1)) {
             onRightDown.Invoke();
         }
         if (Input.GetMouseButtonUp(1)) {
             onRightUp.Invoke();
         }
     }
 
     public void OnPointerEnter(PointerEventData eventData) {
         isOver = true;
     }
 
     public void OnPointerExit(PointerEventData eventData) {
         isOver = false;
     }
 }
 

Now you have new component in your menu at "Component/Event/RightButtonEvent" add it to any UIObject.

This is the way (I think) the new EventSystem would like you to do it. (I got stressed figuring this out and there's no easy documentation, so I'm posting it on the stuff I came across to get to this answer):

 using UnityEngine;
 using UnityEngine.EventSystems;
 
     public    void PointerClickHandler( BaseEventData data )
     {
         PointerEventData pointerEventData = data as PointerEventData;
         GameObject pressed = pointerEventData.pointerPress;
 
         //Left click
         if (pointerEventData.button == PointerEventData.InputButton.Left ) {
             if( pointerEventData.clickCount == 1 )
             {
                 OnLeftSingleClick( pressed );
             }
             else if( pointerEventData.clickCount == 2 )
             {
                 OnLeftDoubleClick( pressed );
             }
         }
         //Right click
         else if (pointerEventData.button == PointerEventData.InputButton.Right ) {
             if( pointerEventData.clickCount == 1 )
             {
                 OnRightSingleClick( pressed );
             }
             else if( pointerEventData.clickCount == 2 )
             {
                 OnRightDoubleClick( pressed );
             }
         }
         //Middle click
         else if (pointerEventData.button == PointerEventData.InputButton.Middle ) {
             if( pointerEventData.clickCount == 1 )
             {
                 OnMiddleSingleClick( pressed );
             }
             else if( pointerEventData.clickCount == 2 )
             {
                 OnMiddleDoubleClick( pressed );
             }
         }
     }

Connect that function through an event trigger on the thing you want pressed (in my case, this function is in the camera, because that works for now, and the EventTrigger was on a sphere in the scene)

What's Going On Here

The EventSystem, which is Unity's shiny new method of doing things, sends events out that get captured by EventTrigger, as every tutorial will tell you. So if you put an EventTrigger on your GameObject, it will respond to press and mouse events.

However, what they don't say, is that all the events the EventSystem generates come with event data that the event gets fired with. All the data from EventSystem events subclass BaseEventData.

If you write a function that takes a BaseEventData as a parameter and place it in a script attached to a GameObject, then when you select that GameObject in the EventsTrigger component, it will appear at the top of the available function list in the editor, separate from normal functions talked about here. The EventTrigger will automatically provide that function with stuff that you can then use. That's what I've done in PointerClickHandler(). It handles all Pointer Click events for the EventTrigger I set.

The StandAloneInputModule, which subclasses the PointerInputModule, uses their own pointer events, called the PointerEventData (a subclass of BaseEventData). The contain the good stuff, like what was last pressed, how many clicks there have been and which mouse button was doing the pressing.

The most useful things to know is that pointerPress tells you what GameObject the press was on and clickCount tells you the number of successive clicks within a certain time-out.