The 8kun Authentigator uses an anonymous email server which requires no registration and no password. However, Guerrilla Mail has been banned by the 8kun administration. The only way to reach it is through a mail forwarder. I tried Bump Email and that worked for a while. 8kun blocked Bump but then unblocked it and instead blocked the proxy server used to bypass the browser cross-origin restriction. That's okay. We don't actually need the proxy. I'm not recommending Bump but I am recommending GMX Mail because it is free and anonymous and it supports mail forwarding (go to the "Filter Rules" section in the email settings). So, how will this work now?
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Expert tip: You can make up your own username if you're careful about choosing something unique. Guerrilla will accept any sequence of eight letters and/or digits. Try it out. In the address input box you can just put something like "abc45xyz@". The domain name is not significant.
Notes on forwarding with GMX Mail: GMX will ask for permission to forward email to the Guerrilla mailbox. Open Guerrilla Mail and click on the button that displays the username. Replace with your own username. Now you can reply to the GMX email. By the way, when you set up the mail forwarding, you should add a filter rule to move the email to the trash. The email address to filter is "noreply@isitwetyet.com".