What I wanted is to have Task Manager start minimized automatically at login and to be placed in the System Tray without showing up on the Task Bar.
This method does not work in Windows 10 and I suspect it does not work in Windows 8/8.1 either (I no longer have Windows 8 or 8.1). In Windows 7, I could easily start Task Manager at login by simply placing a shortcut to taskmgr.exe in my Startup folder and configuring the shortcut to start the program minimized. Solved for Windows 10 Probably also works for Windows 8