When Tweaker is NOT running, I can't move any of the taskbar buttons. When I uncheck all of the Tweaker options, I get the same symptoms (no insertion point)

That doesn't make sense. You should be able to reorder the taskbar buttons when the tweaker is not running - that's a feature of Windows. Also, having the tweaker running without enabled options should not have any effect.

In order to investigate the issue, I need a way to reproduce it. As of now, I couldn't do that with your tweaker settings.

I don't see an image.

Also, could you please answer the questions from my previous comment?

That's unlikely to be implemented in 7+ Taskbar Tweaker, but you can use e.g. winapiexec to show/hide the taskbar:

winapiexec.exe u@ShowWindow ( u@FindWindowW Shell_TrayWnd 0 ) 0

winapiexec.exe u@ShowWindow ( u@FindWindowW Shell_TrayWnd 0 ) 5

You are using a multirow taskbar, right? I cannot reproduce the issue.

Does the issue occur only when the tweaker is running? Does it occur when all of the options are off?

Perhaps you can track the option which causes the issue?

The Windows 10 Anniversary Update is supported by 7+ Taskbar Tweaker v5.2.

The Windows 10 Anniversary Update is supported by 7+ Taskbar Tweaker v5.2.

Implemented in 7+ Taskbar Tweaker v5.2.

Implemented in 7+ Taskbar Tweaker v5.2.

Fixed in 7+ Taskbar Tweaker v5.2.

Closing as a duplicate of:

http://tweaker.userecho.com/topics/420-suggestion-need-delay-before-showing-preview-on-hover/