Do I need to backup my emails from my primary MX server to restore them to a backup MX server?
In relation to setting up a backup MX server, there would not be a reason to perform this in its original configuration.
The purpose of the Secondary MX is to be able to receive emails if the primary server becomes unresponsive so that incoming emails will still reach a server and the original sender does not receive a bounceback message.
As it is not intended to be a fully functioning mail server, making a backup of the emails from the primary server to be restored on the secondary MX server. As for getting any emails that may have been received on the secondary server back to the primary, you would need to seek assistance from the system administrator on a process to implement a method, as there is no function to perform this task.