Reorder email accounts in Thunderbird

To do this without a plugin:

1. Close Thunderbird
2. Backup your profile directory (and most especially prefs.js)
3. 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.
4. 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

You can use add-on Manually sort folders 1.1.

EDIT: Now the link is: Manually sort folders 2.1.1 (TB ver 68+).

2nd EDIT: Since few last versions of TB, currently 91.5.0, you can order account in Account Settings by dragging the account you wish to move.

Since Thunderbird 91, there is an even simpler way without addons and hacks:

1. Right-click any account and select 'Settings' from context menu
2. Drag&drop accounts in the list to the left
3. Done!