The messages indicator only appears when an application has registered to use it; by default, no applications are registered to use it, meaning that the messages indicator is hidden. However, some applications, such as Thunderbird, register with the indicator as soon as you open them and leave no apparent way to remove them.
My solution is to reset the list of applications registered with the indicator to the default (empty), then kill the indicator to refresh it.
Open a terminal and copy/paste the following:
dconf reset /com/canonical/indicator/messages/applications