Turns out temporal fenestrae are not so important in reptile systematics. Removing all characters that reference or compare temporal fenestrae from the large reptile tree results in exactly the same recovered tree.
Contra popular opinion, the large reptile tree demonstrates that temporal fenestra appear several times in the evolution of reptiles.
The synapsid configuration evolved at least five times:
Once in caseasaurs + bolosaurids (including Acleistorhinus and Eunotosaurus) and a second time in traditional synapsids (including protodiapsids), a third time in Lanthanosuchus + Macroleter, a fourth time in basal owenettids leading to lepidosauriformes (but without the lower temporal bar), and a fifth time in nodosaurs and pachycephlosaurs by sealing up the upper temporal fenestra with armor.
The complete diapsid configuration evolved at least thrice:
Once in Petrolacosaurus, its kin and descendants, a second time in sphenodontids + rhynchosaurs and a third time in macrocnemids (including drepanosaurs, tanystropheids, fenestrasaurs and pterosaurs).
The complete euryapsid configuration appeared at least thrice:
Once in Trilophosaurus and again in Araeoscelis and again in Placodus again by sealing up the original diapsid openings with bone in each case.
There may be others.
So when Benton 1982, echoing all standard textbooks up to that time wrote: “The reptiles are divided into subclasses according to the number of openings behind the eye sockets,” he reflected hypotheses that linger to this day. Like the problems that overemphasis on the ankle and calcaneal tuber produce, temporal fenestra should be considered as just another trait, not an overriding trait.
And I’m not even considering those taxa that completely lose the temporal bars that define temporal fenestra in other reptiles.
On another note…
Earlier I was happy to present a postcranial model for the rhynchocephalian/proto-rhynchosaur Priosphenodon. Further study indicated that the manus and pes were switched on the model based on sister taxa. I am told that the artist was not supervised. The posted image has been updated to demonstrate the evidence.