I think, it is impossible to do it in advFind.incident.search or in formatCtrl. Any expression, you put in the initial Expressions section will not be shown in screen. i assume, it depends on the dynamical build of Advanced Filter, and the format ctrl will not be used there (or used AFTER initial search).
But I was successfull, by doing it via the init process: - go to object probsummary - in field Search state press F8 - In State Definition (im.search) go to field Init Process (cc.search.init) and press F8
Now you are in the process, which is executed first on any incident search. But keep in mind, that this process is also used for interaction search.
In Section Initial Expressions of cc.search.init I added this expression: if (filename($L.file)="probsummary") then (flag in $L.file=true) (flag is the field, which is set by the system, if the Button "Close" has been pressed).
This works fine, but has the side effect, that he is searching always and only open tickets.
To adjust this I added a boolean field "Ticket is open?" to form advFind.incident.search with the input value: flag Now, if a user searches for incidents, in his search form he will see, that he is is searching for open tickets only. If he wants to see only (!) closed tickets he has to uncheck this box.
(I did not find any way, to default the flags in the "More" Tab of FilterAdvFind. This would be a more comfortable way).