A distant relative got in touch with me the other day, who is descended from another branch of the Beringer family. She is descended from Katharina Beringer, who is my 3x great aunt. Katharina's half-brother Adam Beringer is my 2x great grandfather, the one who emigrated to Australia in 1884, with his wife Caroline and brother John Valentine (also half-brother of Katharina).
Previously the only information I had for Katharina was that she was born in Rauenthal on 13 July 1845, and had her confirmation in Rauenthal on 23 July 1862 when she was 17 years old. Now, having contact with her descendant, I know that Katharina was married to Philipp Kneip on 13 April 1868 in Rauenthal. I also now know that what I suspected was true: Katharina (and her husband Philipp) managed the Lochmühle (a water mill) in Rauenthal after the death of Valtin Beringer, Katharina's father, in August 1867. In 1871 the Lochmühle was then passed on to Georg and Karoline Koch, as noted in this post.
Katharina and Philipp Kneip had seven children, the first two, Mathilde and Josef were born in Rauenthal (11 November 1868 and 19 March 1870 respectively), the next two, Robert and Adam, born in Schierstein (5 October 1871 and 4 Dec 1873 respectively). After that the family moved north, with quite a bit of time spent in Dillenburg apparently.
It is interesting to note that although Katharina and Philipp were married in April 1868, they were "together" before that as Mathilde was born in November of the same year. If Mathilde was carried to term, conception would have been in about February of that year. She was made legitimate by the marriage of her parents before her birth.
So the question remains: Why did the extended Beringer family give up the mill? The Kneips didn't stay long in Schierstein - Philipp's brother was apparently already running the Grorother Mühle there, but perhaps they stayed with him while they worked out their next move...
Many thanks to my relative for her assistance with the Kneip family information.