Modify the backup or backups that you want to delay and add a custom tag to them such as "Delay Ticketing" and click Add New as shown below. 

Click Submit: 

Then go to Automatic Ticketing and edit your existing profile to exclude this tag from creating tickets: 

Click on Exclude tags section and select the Delay Ticketing tag and Save the changes. 

Then create a new ticketing profile with the parameters you'd like and select the status of Failure and No result at a minimum and in the tags section add "Delay Ticketing" to it. For this one you would turn it on and set the time zone and the later send time to create the tickets later in the day. Example 1400 would be 2pm.