I'm working on developing the extent of how much an observation I made is true; that Phalacrocorax skulls lack a foramen that other cormorants tend to have. Some individual specimen of non-Phalacrocorax species also lack this opening, so it wouldn't be true that the lack of a pronounced foramen confirms that a skull is Phalacrocorax, only that the presence of a forman excludes Phalacrocorax.
From https://collections.nmnh.si.edu/search/birds/?ark=ark:/65665/30edc701b00174dc28a138d9f41032441
From https://virtual.imnh.iri.isu.edu/Osteo/View/Double_crested_Cormorant/570
From http://shearwater.nl/index.php%3Ffile=kop83.php.html
Phlalacrocorax carbo:
From https://www.biolib.cz/en/image/id32230/
And... oh...
I had a lot more for this planned, but this seems to of quickly warped things up: