If you check under Closure Rules in Admin you have the option to force time entry. 

Else maybe this is a option, when the ticket is closed/resolved and values are both false you re open the ticket and adding a note saying the agent need to add time.  I haven’t tested this. 

what i miss is the option to enable closure rules for different companies (departments/groups etc), it is not an ‘all or nothing’ on those rules but we have different requirements per entity.