So, we've hit the last of the Institut grand-ducal's list of Luxembourger settlements: Sheldon, New York. Sheldon was founded in 1804, although Luxembourgers did not arrive until the 1830s. All the references I can find to the town refer to it as a German settlement. It sounds likely that the Luxembourgers merged - and intermarried - with local Germans, as they did in many non-Luxembourger settlements.
The Sheldon Historical Society has a very small footprint on the web. Their website, with a few histories of the town, county, and museum, has not been fully undated since sometime around 2004. For recent information, you have to be very careful to click on their landing page. Go off that and you'll find yourself lost. Their Facebook page shows only one post since 2010.
Despite that, I've managed to learn a bit about the Historical Society. Their primary focus is a museum run out of a former school house. They rotate exhibits in conjunction with an annual yard sale. The topics change annually. Meetings are scheduled regularly with breaks over the winter. Locals may have a good knowledge of the area's history, even though the group doesn't maintain a research library. Contact them for more information.