Ok, as I understand, what you need is to show your Thunderbird events in the top panel calendar in Gnome-Shell. So, I presume, the second part, i.e. syncing your Thunderbird calendar to Google is solved for you somehow.
For this you may want to do the following (it is really easy and takes about 5 minutes to do the whole thing):
1) Install evolution and python-evolution (we are going to remove the Evolution later on):
sudo apt-get install evolution python-evolution
2) Open Thunderbird, go to File>New>Calendar, in the open dialog:
- Select On the Network
- Leave iCalendar option selected and enter a location for the calendar your are creating somewhere in your home dir (it is prefferable NOT to use any .something folders, so that you will not accidentally delete it when you, for example, reinstall your system, so keep it in a safe place)
- The path should look something like this: file:///home/Jordan/MyCalendar/jordan.ics
- Then name it something like Jordan's Calendar, and choose the other options as you like
3) Now open Evolution, go to File>New>Calendar (we are NOT going to create another calendar here, but rather just link the Thunderbird calendar we just created to Evolution so that it will be shown up in the Gnome-Shell panel):
- Choose Type = On This Computer
- Name it (it does not have to have the same name as in Thunderbird, but for your convinience you may want to give it the same name as in Thunderbird, i.e. Jordan's Calendar)
- Choose color
- Check Mark as default calendar
- Check Customize options:
- Open the File name dialog and select the same calendar file you created in Thunderbird (i.e. in our example go to /home/Jordan/MyCalendar/jordan.ics)
- (!) Choose Refresh = On file change
- Now you can Apply, and your Jordan's Calendar in Evolution will be synced to Thunderbird's one.
- You may also want to uncheck all OTHER calendars in Evolution, but leave the one you just created checked.
4) Now we are going to check how it works (it should already work for you!). Keep your Evolution open and open Thunderbird as well. Create a today's event in the newly created calendar in Thunderbird... within couple seconds it should immediately appear in Evolution and in the top panel under Today. Now in Thunderbird move (drag'n'drop) it to tomorrow... In you Evolution the event should be immediately moved to tomorrow, and the top panel calendar in Gnome-Shell now shows it under Tomorrow. So, it should work by now.
5) (Optional) You may want to remove Evolution from your system, but there are two things you should leave: Evolution settings and python-evolution. To remove Evolution and keep your settings intact you use
sudo apt-get remove evolution && sudo apt-get autoremove
but NOT apt-get purge evolution! As for python-evolution, it is used by gnome-shell anyway, so just do not remove it.
Now, you may use Thunderbird with the newly created calendar which is automatically and immediately being sync to the top panel calendar.
Just make sure that you have moved all your old calendar events to the new one (export/import), or have it synced to Google Calendar.