Auto-mount of the contained disk-image, when the external disk is mounted
You can create a launchd LaunchDaemon definition with the key “StartOnMount” set to true. This will allow you to have your own script run whenever something is mounted.

Your own script should then just check if “Backup” is mounted without “TimeMachine” being mounted - and if so, mount “TimeMachine”.

You can use the “mount” command to get information on the currently mounted file systems.