Thunderbird only provides explicit NickServ password authentication. In order to authenticate using IRC server password, you need to edit Thunderbird's internal configuration.
First, create an irc account as usual, using your github account name as nickname. Make sure the ssl option is checked.
On the menu, open
Edit->Preferences->Advanced->General->Config Editor, search for
messenger.account.account. You should find a Preference named like
messenger.account.accountN.name with its value your newly added Gitter IRC account.
Due to this bug, Add a new entry with string value called
messenger.account.accountN.options.serverPassword, and put in your Gitter IRC server password.