In order to do what you want you will have to clear your cache, then sign in to each account separately in ABC order.
Even then it would not work for the next time you sign in.
In Firefox the first one in the list will be last sign in name you used.
For example: You sign in as apple. Sign out, then log in as bread. You then sign out of that one and use cake, read the mail and sign out.
The NEXT time you sign in to Gmail CAKE will be the first one in the list when you might want to go to the APPLE account.
Also, if you clear your cache ALL of the remembered names will be deleted and you will have to set it up again. You can choose what to clear and what to keep in Firefox but I don't know which box you would have to uncheck.
You do have an option.
Download and install an email client such as Thunderbird or Windows Live Mail.
For each of your accounts add them the mail client beginning with the first one alphabetically and configure the client to work with Gmail mail servers. Both of the ones I mentioned can automatically configure itself for Gmail.
The list of all your account names will be seen on the left side of the client page in the order you added them to the client. You would then be able to click the account you want to view.
Edited by Queen-Evie, 17 November 2015 - 06:57 PM.