Remove mail menu from indicator-messages
You just need to remove the Thunderbird file from /usr/share/indicators/messages/applications.
/usr/share/indicators/messages/applications/ as explained here, are just text files containing path to desktop file. You can blacklist them per-user:
cp /usr/share/indicators/messages/applications/* ~/.config/indicators/messages/applications-blacklist/
You might need to reload the message indicator app. The following works in xfce (xubuntu)
pkill -HUP -f indicator-messages-service