Your comments

I'll check out the old versions on dropbox.

Ok, regarding the clicking, any click you want me to do is ok.  R-click is ok; I'll just have to remember about it.  Or, maybe you can add a small X in say the upper right hand corner to close the inspector with a left-click.  At least that is more easily discoverable.  It could be there whether or not you have detected focus-follows-mouse, thus perhaps helping a naive user who doesn't realize the window will close when it loses focus.  Though I guess adding visible parts of the UI is more work.
I agree that it would be inelegant to add button(s) to the inspector.

The thing is, I did not notice this problem with the previous version of tweaker that I was using, so I'm wondering what changed, because I did not change my Windows settings that it's interacting with.  This makes me think that you have changed how you deal with focus, or you have changed how you put inspector on the screen relative to how Windows handles menus.

(Maybe I should try installing an older version to see if I can confirm what I am claiming, but I don't know where to find older versions, since installing the new one clobbered the old one.)

The trouble with checking for the focus-follows-mouse setting is that if MS changes how they store that, the fix will no longer work, but if you want to do it that way, I have no problem with that.

I would prefer that any click, not just right click, on empty space would close the inspector.  My reasons are:

1.  It's one more thing to have to remember about the UI.
2.  R-click on desktop normally triggers a context menu.  Hence, if you do it only on r-click, either the user will get a context menu when they are not expecting it, or might not get one when they are expecting it (depending on how exactly you implement it).
3.  Also, I assume you mean click on desktop, not on a blank area of inspector.  The latter would be bad, imho, since clicking on something usually selects it, not closes it.

As yet another option, what you might want to do is add yet another checkbox to the tweaker menu to toggle exit by focus vs exit by click.  That dialog is already so busy, yet another checkbox would be like a drop in the bucket.  Although I'm not sure whether the win32 api lets you do menus that way.  (Too many years since I looked at it.)

And, yet another option is instead of checking whether focus follows mouse is set, you might instead want to check the menu delay -- which I assume is why I have to move the mouse to the inspector really fast -- and temporarily change it to something longer until focus leaves the inspector, then pop back to original value.

And, thanks for working on this.  This is a very useful hack for me.

--peter