In earlier versions of Unity (now using 2017.2.1f1) I could drag an object from the scene Hierarchy into the Project window and it would create a prefab. This no longer seems to be working for me. I have also tried creating a new prefab and dropping the object onto that, but that doesn’t work either.
I am successful if I drop something simple like a camera/light, but the object I want to turn into a prefab won’t cooperate.
Please see attached video. It also doesn’t work if I drop the object into the tree structure of the Project window.

Your video looks like you’re trying to drag an entire scene and make a prefab out of it. You can’t do that. You have to grab GameObjects, not the scene container.
Maybe you’re getting confused because in earlier versions of Unity before Unity allowed running multiple scenes at the same time, there was no scene container in the hierarchy. At that time GameObjects were at the root of the hierarchy, but that isn’t the case now. When they added running multiple scenes at the same time they added the scene container (so you can keep track of what GameObjects are part of what scene), but the scene container is not a GameObject, so can’t be made into a prefab.
No, it’s just an empty game object, I just gave it a name that ends with “scene”.
Upgrading to the latest version of Unity fixed the problem, though 
Thanks for your time!