That terminology was enough to help me track down the set you saw, which is sold not only in Ryogoku, but in certain shops all over Japan. It’s even sold online at Amazon Japan. The rock is what English speakers would call a flint or firestone, but it’s not actually flint. It turns out there is very little flint in Japan and it’s not suitable for fire making. So, the rock in these souvenir sets is usually meno (agate) or sekiei (quartz), two of the hard rocks that were once commonly used as firestones in Japan.
The steel striker in the set is called a hiuchigane, unless you happen to be from the Kanto area, including Tokyo, where people are more likely to call it a hiuchigama.
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