To do this without a plugin:
- Close Thunderbird
- Backup your profile directory (and most especially
prefs.js)
- Using the built-in config editor (or editing
prefs.js directly), find the mail.accountmanager.accounts preference, and change the sequence of the comma-separated account references in it.
- Find
mail.accountmanager.defaultaccount and change it, if necessary, to be equal to the account you want to come first.
For example, if the value of accounts is account4,account5,account12, reflecting a well-worn profile, and you want the third account to be first, change it to account12,account4,account5. Then change defaultaccount from account4 to account12.
If you aren't sure which account is which, figure out which server configuration is right by looking for mail.server.serverN.name, mail.server.serverN.realhostname, and/or mail.server.serverN.userName (where N are different numbers), and then find mail.account.accountM.server set to the correct serverN.
Inspiration for this answer came from Thunderbird/Change account order