the term "Default Search Dialog" is actually the dialog, the user is choosing from the "Search" main menu, the result list is just connected to the search dialog and probably named "Default Result List". A result list has two parts, the result list itself and the index dialog.
If you want to change the index dialog have first a look at the search dialog and look up the connected result list. You can see this information below the fields of the search dialog after clicking the "More options" link. After identifying the correct result list you can open the settings for the result list. There you find two tabs for "Result" and "Index dialog", choose the "Index dialog" to change the settings there.
I hope this helps.