Right-click the taskbar, Taskbar settings, Notification area, Select which icons appear on the taskbar, turn Thunderbird to ON.

This already on.

If the minimize to tray option is selected in Preferences, the icon only appears in the tray when TB is minimized, and disappears when it's restored. I think that is by design, so the presence of the icon indicates TB is minimized.

The setting I mentioned in my first reply is only relevant for the tray icon that appears when new mail arrives.

Have TB running. Point to TB icon in taskbar and right click mouse. Then left click in the pop up menu; "Pin to Taskbar". Then drag icon to any position on taskbar.

Ok. I wrote the new application for this. Hope it will be useful for somebody else https://github.com/Track77/ThunderbirdToTray