Apparently the best trick is to use an email client like Thunderbird on a local computer. Set up the email in there. Make sure to use POP so the email is handled on the local computer not server-first like IMAP.
Then just let it run I guess! Probably will take a while (days?) for big email accounts. Then you’ve got it locally, so you might consider that “backed up” already assuming you back up your computer.
But you could also “Export” it all as a
.zip file, theoretically.
I can imagine a lot of folks have email archives bigger than 2 GB, and it’m not sure what “back it up by yourself” means exactly, so, good luck?
I’ll also note that I tried doing this a Thunderbird wouldn’t even connect to Gmail via POP for me:
So kind of a fail for me in a 5-minute test. If I was up against the wall here, I think this is the technique I’d choose though. I’d just struggle through finding an app that was happy to set up a new POP connection and get downloading.