Can you make "Add Work" a required before closing ticket? If not can you make it a ticket rule?
There isn't a way to make the "add work" required in the GUI interface. Pinging support to ask if they can do it via an SSH tunnel might be worth a shot.
As far as rules go, thinking out loud, you might be able to look for any tickets that have a null value for work hours and based off of that prevent them from closing the ticket. They try to close it but the rules opens it back up and a comment that indicates you need to add your work hours before you are allowed to close.
What i ended up doing since I could not find a solution was create a report based on how many days or hours the ticket was open for a manager and let the manager figure up the numbers. Like EOD report showing the following.
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