Any reason this doesn’t work? I don’t see why it wouldn’t…

    using UnityEngine;
    using UnityEditor;
    using System.Collections;
    
    [CustomEditor(typeof(TargetClass))]
    
    public class TargetClassEditor : Editor
    {
        public void Awake()
        {
            Debug.Log("I'm Awake");
        }
    }

EDIT FOR CLARITY: How do I set my default values and such when extending the editor class for a custom inspector?

I am pretty sure you should be using OnEnable() instead of Awake(). Since you are extending the Editor class.