Welcome Cypher. I always like seeing family machines brought back into service. We like pictures, too.
I have a Junker and Ruh machine which is a 'spin-off' of Wheeler & Wilson machines made in Germany. I don't know if W&W machines take different needles or not. I know my Junker does take different needles. Fortunately, it had a needle in it which I took to a place here in Denver to check and found a comparable needle that works in it. I'm guessing your machine would take a round shank needle.
I'm not completely sure of when or what machines kept the Wheeler & Wilson name for a while after Singer bought them out in 1905. I have perused some of the images that the Smithsonian has of Singer catalogs for Bridgeport factory from 1908 and 1924. I found that the 1908 Singer Catalog still had W&W badge whereas the 1924 had the Singer name for the 12W102. It appears that it was a "tailor's machine" for a variety of fabrics. The first two links are from 1908 and the last is from 1924.
https://www.sil.si.edu/DigitalCollec...es/image25.htm
https://www.sil.si.edu/DigitalCollec...es/image26.htm
https://www.sil.si.edu/DigitalCollec...es/image29.htm
I couldn't find any parts or instructions for the 12W102 but maybe some of the other 12W pdf files found at
http://parts.singerco.com/IPpartCharts/ and
http://parts.singerco.com/IPinstManuals/ may help.
Janey - Neat people never make the exciting discoveries I do.