Your comments

Maybe it was a temporary Windows issue. I'll close the bug for now, let me know if it comes back.

Since it's not a bug of 7+ Taskbar Tweaker, I'm closing this issue. Let me know if you find out that it's something to do with the tweaker.

I hoped for some information such as the Windows version or maybe conflicting software. The tray icon hiding functionality haven't changed for years in the tweaker, and I haven't had problems with it. Basically, it uses the documented NIS_HIDDEN flag to hide the icon, so I don't see a reason for it to misfunction.

I have verified, and it works on my computer. Do you have a way for me to reproduce the issue?

Just add emptyspace|rclick=2, it should not override Shift+Right click.

Showing the menu is the default behavior. Why would you need an option for it?

I'm not sure I understand the suggestion. What are you referring to as the "standard menu"? The menu below?