How to highlight a GameObject in the Scene view from an Inspector script?

Alright I figured a solution!

Since the OnDrawGizmos() method is only invoked on runtime scripts (not Editor scripts), I went back inside the Script that the Inspector acts on, and put the following lines:

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MonoBehaviour derived class:

 // Above in the USING/ IMPORT statements:

 #if UNITY_EDITOR
 using UnityEditor;
 #endif

 // ... somewhere else within the CLASS definition:

 #if UNITY_EDITOR
     private const float _OFFSET_CROSS_SIZE = 0.1f;
     private static Vector3 _OFFSET_X_POS = new Vector3(_OFFSET_CROSS_SIZE, 0f, 0f);
     private static Vector3 _OFFSET_Y_POS = new Vector3(0f, _OFFSET_CROSS_SIZE, 0f);
 
     [HideInInspector] public GameObject inspectorObject;
     [HideInInspector] public int inspectorObjectIndex; //Optional
         
     void OnDrawGizmos() {
         if (inspectorObject == null ||
            Selection.objects.Length == 0 ||
            Selection.objects[0] != this.gameObject) return;
 
         //Draw a "crosshair" on the selected child GameObject:
         Vector3 pos = inspectorObject.transform.position;
         Gizmos.color = Color.cyan; 
         Gizmos.DrawLine(pos + _OFFSET_X_POS, pos - _OFFSET_X_POS);
         Gizmos.DrawLine(pos + _OFFSET_Y_POS, pos - _OFFSET_Y_POS);
     }
 #endif

........................................................................

Editor / Custom-Inspector derived class:

 public override void OnInspectorGUI() {
     mTarget = this.target as NAME_OF_YOUR_CLASS_HERE;
     
     //Somewhere after the GameObject DropDown list...
     mTarget.inspectorObject = theSelectedListItem.gameObject;

     //Check if the DropDown selection has changed...
     if(lastSelectedListItem!=theSelectedListItem) {
         SceneView.RepaintAll(); //Refreshes the gizmos on the Scene view.
         lastSelectedListItem = theSelectedListItem;
     }
 }

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For example, this would draw a cyan colored cross like this:

^^Preview of Gizmos drawn according to the "Current Layer:" selection in the Inspector