In the Valmiki Ramayan Ashvamuni’s ashram is described as a safe place for Saints. There is a temple of Goddess Ashvamukhi near Sharbhanga Ashram. It’s also believed that the goddess was a brave woman and had destroyed many demons. As per the research work and sequence of places visited, this is surely the Ashvamuni’s Ashram.
Valmiki Ramayan 3/116/20, 21, 22