Having a good backup routine is important. It’s also important to monitor your backups. By this I mean to check that your backups are successful, and know what your latest good backup is.
Recently, I had a customer have a disk drive fail. The system was successfully restored, after a new drive was installed, but quite a bit of time was lost searching for the latest good backup. I had to go through the backup tapes one-by-one, and find the latest good backup.
If you have a rotation of several tapes, as you should have, you need to keep a log of the date and result of the backup they were used for. If you are using the common rotation, of a tape for each day of the week, then you need to note if a tape did not get changed, or used on the day that it is marked for.
The majority of your backups should be successful, if your tape drive and system are working properly. A simple system is to mark down the times that the backup is not successful. Using an online table or spreadsheet is preferable. It can be backed up and sorted, etc.
So, something as simple as a note on the tape if the backup is not successful, or if the "Tuesday" tape was left in, and has the "Wednesday" backup on it, will work. Put simply, at any point in time, you should be able to pull out your last successful backup, and not have any question about which one it is.
An automatic eject after a backup can be helpful in preventing inadvertent reuse of a tape. You can have your backup program email you requesting help with a tape mount.