After being defeated while using a bo (long staff), Muso retired to a cave on Mt. Homan to meditate upon his defeat and how to better his art. Upon reducing the size of a bo to that of a jo and developing waza (techniques) that controlled seigetsu (solar plexus) it is said that another duel between Musashi and Muso occurred in the castle town of Himeji, where the jo broke the famous two sword block known as "Jujidome".
The cave used and kept today as a shrine for Muso was used by many wandering warriors practicing shyugyo (austerity rites). They would live in seclusion to train and meditation and forge their spirits.
Musashi was eventually hired and worked at Kumamoto castle as a kenjutsu (sword) instructor into his old age. For those of us that do Jodo, the Kuroda Han is not too far away geographically. It will be interesting to see if any verification of a meeting or a duel between Musashi and Muso Gonnosuke can be substantiated.