Hi Lamak, my name is Neil, I'm an independent adviser for Microsoft and a Windows user like you.
Have you tried pinning the Task Manager to your taskbar?
Open task manager and then right click on the icon on your taskbar and choose pin to taskbar.
This will ensure that task manager is always there and just a single click away to open.
I will try and find out about loading it in your system tray if it is still possible.