JayCee,
The gun was made in Birmingham almost certainley by J.P.Clabrough for J.J.Simon.Chicago.
Patent #397 was registered on 29 Jan;1881 to J.T.&J.Rogers,gun action filers working for the trade,located at 78 Lower Tower Street,Birmingham.The Rogers brothers obtained U.S. patent #257.764 in 1882,which they assigned to J.P.Clabrough who had manufacturing cability in Birmingham coupled with a strong U.S distribution dealer network based in San Francisco.
The proof marks are Birmingham Black powder.The Not For Ball mark tells us the gun was made between 1875&1887.
I can find no information On J.J. Simon,Chicago.
Many of Clabroughs early hammerless guns featured the action shown in the photographs.
Roy