Just as you opinioned Mr. Day was born near 1830 and died in the late 1800’s. Other than the following rather sparse information found on Ancestry.com there is not much else on him. It is interesting that his occupation is listed as “Inventor” which, of course, keys in with the patent records you found.
Born: About 1826-1828, Belvidere, Warren County, New Jersey, USA.
Died: 5 August, 1880, Age approximately 52-54. Buried in Union Cemetery - Hackettstown, Warren County, New Jersey, USA.
Never married, no record of military service.
Occupation: Inventor
Grave marker:
http://image1.findagrave.com/photos250/photos/2008/30/24298400_120183083195.jpgLooks like a modern stone - a Mr. Michael Holmes took the photograph, he seems to have an avocation of photographing grave markers for other people doing ancestor research, so, no relation to Joseph Day and I could not find a record of anyone in contact with Mr. Holmes regarding why the photograph was taken.
If this is our guy, and quite likely it is, he left not much of a trail.
Once again, thank you so much for your help.
dave