Does the flag ship just stay in port?
I don't think it's unusual for the flagship in a home port to be laid up. Think about HMS Victory at Portsmouth for instance.
It's possible that he was nominally assigned to Impregnable but resident in barracks onshore, or serving in smaller vessels operating out of Devonport.
I have considered this as a possibility. He does seem to be somewhere...
Interestingly, I heard from a descendent of the captain of HMS Royal Adelaide from the 1880s. That was a flag ship but was laid up and his family lived aboard - his wife even gave birth on board.
