I'm not even sure what the objective is here. When the System Tray is opened with JAWS Key + F11, you can use first-letter navigation to find anything. Is it that critical to have the icons arranged in a certain order if you're using JAWS?

On Sat, Mar 16, 2019 at 10:10 AM, Steve Matzura wrote:

You want to rearrange system tray icons. This is not possible.

That is not technically correct.   I still haven't found a way via the keyboard, even using emulated drag and drop, but it can be done via actual drag and drop.  If something is driving you absolutely mad because it's "too far down the icon parade" on the system tray then if you can get a sighted assistant they can drag it to any position relative to the other displayed icons you wish.
 
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Brian - Windows 10 Home, 64-Bit, Version 1809, Build 17763  

   Explanations exist; they have existed for all time; there is always a well-known solution to every human problem — neat, plausible, and wrong.

         ~ H.L. Mencken, AKA The Sage of Baltimore