Only today realised that while I have been able to integrate my gmail calendar with my Thunderbird in Ubuntu, my tasks are missing.
Apparently that needs an another add-on, which is still in beta but claims to work pretty seamlessly.
add-on: Google Tasks Sync 0.4.1
Now in the Tunderbird Task tab, on the bottom right, I have a pane that says: Click here to get started
So, clicking that link opens a window where you are reqd. to allow the add-on to access your gmail account and then click on ALLOW ACCESS in the next window so the add-on can access your gmail account. The tasks are there now and I can add or delete tasks. It works the same way as in Gmail calendar.
But, the New Task icon is greyed out. And if I open the Task tab, the whole area in the center—I don’t know yet what iti sfor and is empty. Gmail supports tasks with description and due date, so I do not know what is the issue. Will get back when I have more info.