Gmail finally allows you to be logged in to multiple accounts at the same time.
You can switch between them from the top right by clicking your email address, and then ‘Switch Accounts’ (see adjacent picture).
However, when you open a new tab/window and go to gmail.com, it will go to your default Gmail account.
Google makes the first account you logged into your default account.
So, it looks like right now the only way to change your default account is to log out and log back in with the account you want to be the default first.
Let me know if you find another workaround to this faux pas.