Hello Matt. Don't know if this will help any or not, but owning a few different Cadillacs from the 1980s era, I have some observations I can share about the GM factory coach lights, which they called opera lights.
Having seen your car in person in Flint, I can tell you that those are standard issue Cadillac opera lights, and that someone, most likely the assembly line worker at Eureka, did put them on the wrong sides of the car. As installed on the factory Cadillac passenger cars, the lights are intended to angle rearward at the top, but the top and bottom edge are supposed to be flat.
In yet another example of auto maker stupidity that makes no sense, I have identified three different types of the Cadillac opera light, even though they all look the same.
The earliest version had an outside set screw on the bottom, that allowed you to remove the lens to access a replaceable light bulb inside. Removing the lens also revealed two simple ordinary screws that attached the light to the car.
That morphed into a very similar light, except that the set screw disappeared, and the light was now mounted to the car by running a nut up a pair of studs from the inside of the car. Since these are not required lights, no provision was made for being able to replace the bulb. Think of them as being a sealed beam opera light.
That style changed yet again to another very similar version, the difference being that the bulb was replaced with an electro luminescent panel that simply glowed when electricity passed thru it. When that version would finally burn out, there was no replacing them at all. If you wanted working opera lights with that version, you replaced the whole unit.
Fortunately, however, these three versions are interchangable with each other, and as so many 80s Cadillacs were built, finding them in junkyards seems to be pretty easy. Whenever I come across a junkyard car with the first version opera light, with the set screw and easily replacable bulb, I grab them. As my opera lights have burned out and needed replacing, I have replaced them with this style, so that future bulb replacements will be a simple matter.