I was looking up Richard Roth's in Pennsylvania or New York state (long shot, but tried it), and looked up Frank, and the approximate date of birth of Richard. Found Richard's burial with mentions of Frank and Ethel there also! right time periods, and right placement. In addition, found Frank's burial beside his first son. Within the cemetery listing, Forest Hill Cemetery, there were other family members that were linkable by parents. A few of the family members aren't quite as clear as Frank and most of his siblings, but I decided that I could look further into the family by checking back to censuses.
I did not check previous censuses originally due to there being too many Frank Roth's living in the United States at that time. Roth is a typical name of Germany, like Smith or Jones are thought to be in the United States. Searching for more of Frank Roth when there was only the one census connection to Ethel kept me from making further progress that way. Also, since the census containing Frank and Ethel was the 1930 census, there was no way to move forward with further census searches in 1940 as that census is not yet available.
From the information jackpot gathered from the Forest Hill Cemetery, I was able to go back to the censuses and make a good search from 1930 backwards to 1900. Since the 1890 census is almost non-existent, that would be out of the question to search. Unlike my Forson relatives (Dennis Sweeney in particular), I have not yet come across any other relatives who would be part of the Civil War enumeration of soldiers that survived the Civil War. There may be a Roth involved, but the Ancestry search engine did not turn up anything there, and there is lower likelihood to find something unless I were to proceed farther back in time with more-specific ancestral aim of a person who I knew was alive then and would be of an appropriate age.
I went through the 1920, and 1900 censuses for Frank, keeping an eye out for brothers and sisters as I went, collecting his older sister Barbara and her husband. then I started with Frank's father and mother, William and Josephine Roth. Progressing backwards in time yielded various children, and gave me the information that I should be looking for 12 children, 8 of whom were living. Since finding that census, I have now 10/12 children by name. There is one possible child from the Forest Hill Cemetery, but no proof of relationship. I want to find those other children, but at the same time, I need to track the possible parents of William (Peter Roth and either Eunice or Esther or unknown wife #3) to see which child may belong to whom, and to flesh out their generations as far as possible before presenting evidence to relatives.