The quadratojugal is the cheek bone that connects the jugal to the quadrate in most reptiles. Typically the quadratojugal is ventral to the squamosal. According to the large reptile tree the quadratojugal disappears or nearly disappears (without becoming fused to another bone) and then reappears in the following taxon pairs:
Disappears: Paliguana and most basal lepidosauriformes
Reappears: Sphenodon, Mesosuchus, Hyperodapedon and other rhynchosaurs
Reappears: Macrocnemus (including tanystropheids and fenestrasaurs, including pterosaurs)
Becomes a vestige: Stenocybus (semi-reduced) and therapsids
Disappears: Wumengosaurus (and most thalattosaurs)
Reappears: Utatsusaurus and other ichthyosaurs
Disappears or Nearly Disappears (remnant on the quadrate?): Largocephalosaurus and Sinosaurosphargis
Reappears: Helveticosaurus and Vancleavea
Reappears: Palatodonta (and the placodonts)
The fact that the quadratojugal reappears in so many clades demonstrates the genes remain present, but turned off in taxa lacking the quadratojugal.
The fact that the lower temporal arch disappears then reappears demonstrates this trait does not strictly define clades and does not restrict clade members lacking the quadratojugal from inclusion.
In certain cases it is also true that the quadratojugal is hard to identify if present in crushed and disarticulated fossils.