The reason there's no backup option in account mode is that there's nothing to back up. In account mode your keys are generated every time you login using your password, just like on Steemit.com.
In wallet mode your keys are stored in a browser database which is just unlocked with your password. When in wallet mode you absolutely need to create a backup file or write down the brain key.
There's no reason for you to be switching back and forth between account and wallet mode.
RE: Funkit's tips and tricks with Bitshares light app #2 The backup conundrum