You have an option to display an Icon in the System Tray (for Windows at least), but I don't see any way to minimize to the tray to remove the Task Bar entry as well. Is there a way? Not being able to minimize to the tray seems to make the tray option somewhat irrelevant.
I see this is already a feature request (ID 1431501).
Yes you are right tst does not have "minimize to tray icon" feature. And there is a feature request for it.
At present, tst uses tray icon only to show application update announcements.
In future, we will add "minimize to tray", icon's menu.