Elgin is one of the great American bicycle brands. The internet has its fair share of sites devoted to classic Elgin bicycles, my favourite model being the Elgin Miss America.
The Elgin brand seems to have originally been something to do with either the Elgin Cycle Company or the Elgin Sewing Machine Company or even the Elgin Sewing Machine and Bicycle Company all based in Elgin, Illinois and active in the 1890s.
Shortly afterwards the Elgin brand was owned by Sears, Roebuck and Co. the iconic American catalogue retailer based in nearby Chicago, Illinois. Sears used the Elgin brand up until around 1941. Sears seemed to have had Elgin bicycles manufactured for them by a tangled web of different companies representing many of the great names of US bicycle manufacturing.
One manufacturer was George Huffman’s Davis Sewing Machine Company of Dayton, Ohio. In 1924 the Davis Sewing Machine Company got into financial difficulties and was taken over by The Huffman Manufacturing Company (also owned by George Huffman). The Huffman Manufacturing Company introduced their own, infamous, ‘Huffy’ brand in 1934.
Another manufacturer was the Westfield Manufacturing Company of Westfield Massachusetts, which became part of the Columbia Manufacturing Company owner of the famous ‘Columbia’ bicycle brand.
After the Second World War Sears does not seem to have used the Elgin brand for complete bicycles.
In terms of derailleurs, I believe that Sears used Elgin American derailleurs on some of its own-label Free Spirit models, particularly those manufactured by Murray in the 1970s. I do not know if there was more than one model of Elgin derailleur.
Elgin American derailleurs were manufactured by Excel (who were based in Elgin, Illinois). There is a strange synchronicity between Excel Dynamic being a belated copy of the obsolete, French, Huret Allvit and the Elgin American being an equally belated copy of the obsolete, French, Simplex Prestige. Nostalgic Francophiles were clearly on the loose in Elgin, Illinois.