The Wild Goose Mystery (upd. Cilde Harold Willis)

One point of clarity to Greg's otherwise fine historic thumbnail sketch: The cars were manufactured in Marysville, Michigan on the banks of the St. Clair River, about 60 miles north of Detroit, rather than the banks of Lake St. Clair. My spelling of "St. Clair" is correct; Mr. Wills added the trailing "E" to both words in an attempt to perhaps make it more aesthetically pleasing.

The Wills Sainte Claire motorcar was quite inovative in several ways. Designed by Childe Harold Wills, he incorporated molibdimum steel and unique design features in his creations. Wills was significantly responsible for every car design by Ford from 1903 to 1919. He decided he wanted to produce and design a high-end car with small proportions and great performace and luxury - the opposite direction Ford took his company. With a HUGE severance package ($millions in 1919 money) Wills left Ford and started his own company on the shore of Lake Sainte Claire just north of Detroit Michigan. In fact he developed a whole town/company concept that provided everything his employees could possibly need to live and work an idealic life without leaving the site.

In 1920 the Wills Sainte Claire motorcar incoprorated the side coutesy light afore mentioned, hydrolic drum brakes (first produciton car to have them), overhead cam v8 engines driven by sprirel bevel gears, and a back-up light when reverse was engaged (first car to use this feature).

Unfortunately C. Harold Wills was too much the perfectionist and too much the car designer to be a good businessman. He persistently stopped the production line to incorporate pregressively new improvements to his car - it was just not a good way to do business. He eventually went bankrupt producing a car design ethic that Mercedes Benz would eventually becomne known for in the post WWII era - well designed, efficiently packaged, luxury cars.

This light is to illuminate the runningboard for people entering and leaving the car at nite. A nice little detail. Other makes had a light for similar purpose but the Wills one is used as a unique design feature.

Courtesy light:
http://archive.org/stream/automotiveindust46phil#page/224/mode/1up/search/claire
A good techical descripton of the Wills Sainte Claire in the same journal, Automotive Industries:
http://archive.org/stream/automotiveindust45phil#page/912/mode/2up/search/Wills+Sainte+Claire

Without really knowing I'd say it's a form of courtesy light and judging by the way it's aimed it appears that the intention is to light up the area adjacent to the car, rather than the running board. With the door open the running board wouldn't get too much illumination. If memory serves the Studebaker Big Six also had a courtesy lamp. Another interesting feature of the Wills St. Claire is the style of the combination headlamps and marker lamps - very European...