Should be fixed for Windows 10 versions 1809 and 1909 in the latest beta version, 5.7.1.2.

Still investigating Windows 10 version 1803 (build 17134.1099).

That's already possible by using advanced options.
Open the Advanced Options Editor (more details), and add the following value to Mouse Button Control:
Name: taskbaritem|rclick
Value: 2

See the help file for more details.

102 is a known issue. Please see my reply here:

http://rammichael.com/7-taskbar-tweaker/comment-page-17#comment-3660

There's no error code with the number 120. Are you sure that you provided the exact error message?

Also, please provide the tweaker version you're running and the version of your explorer.exe file, found in the C:\Windows folder.

The configuration is kept unless you check the checkbox to remove it when uninstalling.

You're probably experiencing the incompatibility caused by the KB4517211 update. The latest version of the tweaker, v5.7.1, fixes compatibility with this update. Please make sure that you're using the latest version of the tweaker, and let me know if you need more help.

Thank you for the detailed reproduction steps. I'm aware that the virtual_desktop_order_fix option doesn't always work. As far as I know, it works well when grouping is disabled, and doesn't work when grouping is enabled for grouped items which are spread between virtual desktops (like in your example, the explorer group which is spread between VD 2 and 3).

See also the discussion here:

https://rammichael.com/7-taskbar-tweaker/comment-page-40#comment-10468

As I wrote in the comments in the link above, I'd like to look at it one day but don't plan to do that in the near future.

The core of the issue is that when labels aren’t displayed, and either there’s only one item in the group, or the group is combined, the “group icon” is used instead of the actual window icon. Currently 7+ Taskbar Tweaker doesn’t provide a way to customize this behavior.

You probably meant 102, not 104 in the title? Please see my reply here.

Closing since the issue is very old, no other users reported about it, and the investigation stopped. If the issue is still relevant and you have more information, or would like to try other things to try and understand what's going on, let me know and I'll reopen the issue.