According to the Missouri Death Records, 1834-1910, for the week ending October 1, 1864, I found an entry for Joseph M. Hollinback. According to this record, Hollenbeck was born in New York and died at the age of 27 of chronic diarrhea. Confirming this, there is the St. Louis City Death Records, 1850-1902, which has an entry for Joseph M. Hollinback, born in New York, who died on September 26, 1864 and was buried at Wesleyan Cemetery.
I need to run down the burial records for Wesleyan, a Methodist cemetery in St. Louis that was moved several times before closing in 1952. Hollenbeck would have been buried at the second version of the cemetery that was open between 1851 and 1878 and was located at Grand and Laclede.
But I'm very comfortable right now stating that Joseph Hollenbeck was born in New York around 1837 and died in St. Louis in September of 1864.