What doesn't work:
Settings/Accounts and Import/Import mail and contacts - you can't import from another Gmail account!
Settings/Accounts and Import/Check mail using POP3 - although you can set up reading another Gmail account via POP3, the Gmail server will not let you leave the read mail on the server. So you can use this to move mail to another account, but not copy it.
Settings/Filters then setting up a filter that catches everything, telling Gmail to forward it to the other account, and saying 'apply this filter now to all those existing messages' - it simply doesn't forward them although it will do other things to them all, like apply a label.
At the moment, I am pondering setting up a third account, then on the backup account, set up forwarding of all incoming mail to the third account, then use POP3 to get all the messages from the original account.
This will empty the original account (boo) but should result in there being two copies of everything: one on the backup, one on the third. Then on the original account use POP3 to read the third account.
Madness, but it might work...
Any other suggestions? Gmail's help doesn't seem to think that anyone might want to backup a Gmail account.
This entry was originally posted at http://lovingboth.dreamwidth.org/396812.html, because despite having a permanent account, I have had enough of LJ's current owners trying to be evil. Please comment there using OpenID - if you have an LJ account, you can use it for your OpenID account. Or just join Dreamwidth! It only took a couple of minutes to copy all my entries here to there.