I'm very new to Ubuntu so please bear with me. On the latest Ubuntu (12.04) I have set up thunderbird to read my Gmail account. I know there are browser addons that show you how many unread emails you have, but is there a way I can get this integrated with the Unity Mail icon on the top bar?
Not too sure why this is happening but can you please try setting Thunderbird as the default mail client.
You can access this in SETTINGS, then click DETAILS (in SYSTEM Section), then click on the Default Applications from the left list and change Mail section to Thunderbird.
Restart and check if it's working now.
Let me know if this worked as I don't have a sure answer but think it has something to do with default applications and would be nice to know.