Instead of adding an attribute, and therefore another field for your technicians to worry about, perhaps you could just create a new Ticketing Status of "1st call resolved" (or whatever you want to call it).
As long as institutionally you have a clear definition of when this status would be used it should give you what you want.
To do this you would go to ADMIN>Ticketing Applications>Specific Application>Statuses>New
I imagine you would select "Completed" for the Class.
Hope this helps,