I just learned that the Badges option needs to be turned off in order to 
rearrange the System Tray icons and here are my corrected steps:
Settings and their state:
Lock the Taskbar button, On.

The next several options I have Unchecked / Off.

Taskbar location on screen Combo box, Bottom

Taskbar location on screen Combine taskbar buttons, Never

Here's how I rearrange the system tray icons  running Windows 10 Pro Version 
1809 (OS Build 17763.379) & all installed versions of Jaws.
1. Windows key + I, for Settings, tab 1 time to System, right arrow to 
Personalization, and press enter.
2. Navigate to, Taskbar and press enter.
3. Tab several times to, Show Badges on Taskbar..., and make sure this is, 
Off / unchecked.
4. Tab a few times to, Notification Area, Select which icons appear on the 
taskbar Link, and press enter.
5. Okay now to put the System Tray in the order you want it in.  Tab through 
all the icons making a note of which ones you have checked / turned on 
because you're going to uncheck all of them.
6. Uncheck all the icons.  Now you will go through and check the icons in 
the order you want them in but keep in mind, they will appear in the reverse 
order that they are checked.  What I mean is, the 1st one yu check will be 
at the bottom of the list, the 2nd will be 2nd from the bottom, the 3rd will 
be 3rd from the bottom etc. etc....  After you're done open the system tray 
to make sure it's the way you want it and Alt + F4 if it is.

Note:  With the System Tray now arranged the way you want it, you can now 
turn, Badges, on if you prefer this setting to be on.