Have you tried setting this at settings>general?

Thanks David for your quick response. I had not noticed that feature before! Under Settings > General > Incoming Mail > App icon options, there are two check boxes (count of new or unread messages), with the 'new' checked by default. So, why nothing previously? Well, I sent a few messages to myself:

With count 'new' checked: If I send a message and minimize TB to the Taskbar nothing is shown until TB is opened and even then not until 'get message' is clicked. But is displayed for only a few secs since New Alert > Customize new mail alert is set at 30 sec by default.

With count 'unread' checked instead: once again, nothing is shown while TB in minimizes and until Get Message is clicked! Even worse, If I then minimize TB to the taskbar the number of unreads is not shown in the Taskbar, as expected (above), but if TB is then re-opened (click taskbar icon) no count is shown even if Get Msg is then clicked !!

This seems to be a bug (?) since (1) there is a need to see the count on the taskbar icon only if TB is minimized - otherwise it is obvious from the opened app. (2) looks like TB wont import (get) messages until the 'Get Message' button is clicked. Is that true ?!!

The issue still needs help. Thanks, Robin

I have the same problem. You can turn on Count in the New Message drop-down at the top of the Folders pane, but that seems to apply to the counts in the Folders. In Settings/Chats, there is Notifications section where you can select Show the notification and Flash the notification. I am not sure what Flash the notification means, but it doesnt show a new message count on the taskbar icon. I also went to App Icon settings where you can customize Alerts, but there are only 3 options and Show Count is not in that list.