Starting in 1914, Pierce-Arrow headlights were placed on front fenders using an odd, vaguely trumpet-shaped stalk. This definitely made most Pierce-Arrows visually distinctive. I used the word "most" because not all Pierce-Arrows had that feature. According to Richard Burns Carson in his book "Olympian Cars," (p. 194):
"Pierce-Arrow management rightfully credited their products with having the most famous headlights in the world. The Pierce-Arrow was universally known as that marvelous large car with headlights coming up out of the fenders. After this feature was patented and introduced in 1913 it appeared as a hallmark on most future Pierce-Arrows cars, but because these wide-stance headlights were illegal for many years in Pierce's home state of New York, the company offered an optional package of conventional bracket-mounted headlights. Even after New York withdrew its objection to the fender headlights some customers continued to prefer the bracket-mounted option that was still available into the early 1930s. When so equipped, the marque lost much of its memorably imposing appearance...."
But I think the Pierces with conventional headlights looked a lot better without those awkward headlight stalks.
This issue gradually became moot by the mid-1930s. In order to stay in synch with styling trends, Pierce-Arrow cars got fatter fenders and the headlight assemblies became more merged into them. I can speculate that had Pierce-Arrow survived to the 1940 model year, its headlight arrangement would have been essentially indistinguishable with that of the rest of the cars in the American market.
Below are some examples of Pierce-Arrows with traditional P-A headlights along with images of Pierce-Arrows with conventional (for the times) headlight assemblies.
Traditional Pierce-Arrow Headlights
Pierce-Arrows with Conventional Headlights