It is worth noting that the field guides I read suggest altogether different field marks for the Black Swallowtail. Also, my pupil-in-the-iris shortcut only works because here in Louisiana we do not have the other western swallowtails with that same marking.
Many people who know more about butterflies than me (as there are many many people who know more about butterflies than me), point to the parentheses-shaped markings and the second row of spots as diagnostic.
These field marks are helpful when they are all there, but sometimes they aren't.
Moreover, sometimes, the Eastern Tiger Swallowtail dark morph has markings that could be mistaken for Black Swallowtail parentheses.
As for the pupil-in-the-iris, it is also found on the Anise Swallowtail, Indra Swallowtail, and Old World Swallowtail. The Old World Swallowtail has a subspecies called Baird's that looks remarkably similar to a Black Swallowtail. These species are western and are not found in Louisiana.
There is a section of the U.S. where their ranges overlap with the Black Swallowtail. If you live within the red rectangle, then you certainly cannot count on the pupil-in-the-iris to be diagnostic.