In 1850, Aaron and his four brothers were in the household of their mother, Salina Hartman Nelson. Aaron was the only one working: 'in factory.' If his birthdate is correct, he was born 2 years before the marriage of Salina and Andrew Nelson.
If the age is correct, no way to tell if he is Andrew's child, or Salina's, or if they are both his parents. We find no evidence of him after the 1860 census. I wonder if he can be the Aaron Pierson who appears in 1870 in Groveville with wife Nancy, and whose family seems always to be nearby the Nelsons, right up til the time of World War II, when my grandmother had a 5" x7" studio photograph of Lester Pierson in her home.
When 'Old' Andrew Nelson's property in Upper Freehold Twp, by that time Jackson Twp, Ocean County, was finally sold, the deed was signed by Young Andrew's sons Joseph, James and Henry. Aaron and William were not there.