The attached link will take you to a brief history of the Baker Gun Company.http://www.bakercollectors.com/index.php?p=1_7_History-of-the-Baker-Guns
the best place for gun info would be cabelas gun library.
Blue Book of Gun Values
Wilmot Gun Company was a trade name made by Henri Pieper in Belgium c. 1877-1914.
Blue book of gun values
Made sometime between 1905 and 1931. They were made by the Baker Gun Company in Batavia New York.
Look in "The Ithaca Gun Company - From the Beginning"
You can find information about an American Gun Company Knickerbocker shotgun through online firearm forums, gun enthusiast websites, and auction sites that specialize in vintage firearms. Additionally, resources such as the Blue Book of Gun Values or historical firearms reference books may provide detailed information. Local libraries or museums with firearms collections may also have relevant information. For specific inquiries, reaching out to collectors or gun appraisal experts can be helpful.
You can find out @ when it was made/shipped and other data depending on what, if anything , has been published by the company.
UMC refers to Union Metallic Cartridge company. They are owned by Remington and only make ammunition not firearms.
Have you tried the Internet?
Try e-gunparts.com, gun shops, gun shows, want ads.
I posted a link in the related links section that may be of some help.