By default, a Mozilla program doesn't have a password, anyone who has access to your system can launch any of the Mozilla products installed. It's unclear what passwords you're referring to.

If you never used Sync before, you need to create a new account.

By password, I'm referring to the username/password combination I set up to log in to this help page and the Thunderbird help page. This is saved in 1Password as "Mozilla" and is to be used for ALL Mozilla-related log-ins.

My user name is very unique so I'm surprised that it may be in use by someone else.

OK, I used a variation of my default username. Unfortunately I was not given any option to save it in either Firefox or 1Password.

I highly doubt that a username / password saved in 1 Password is going to be available for and used by Firefox Sync (which uses an internal chrome:// address, which an external program doesn't have access to).

To get your Firefox Sync Username / Password, and Secret Phrase password saved into the Firefox Password Manager, you might need to disable 1 Password temporarily.