Terutoko Shrine is located in the middle of a small, low, wooded hill in the suburbs of Matsue northeast of the castle.
It is listed in the Izumno Fudoki, meaning that it existed a millenia before Matsue and its castle were built. Then it was known as Arawahi-sha.
Later it was known as Teratoko Shrine, and the kami was Teratoko Myojin.
In the Meiji Period its name was changed from Teratoko to Terutoko, thereby removing the reference to temple in its name. The kami was renamed Amaterasu, a common occurrence during the creation of the new imperial-centered state religion. many kami were renamed to bring them under the umbrella of imperial lineage.
2021 Update
A recent look on googlemaps shows that the path I took through woodland and bamboo to reach thye shrine has now gone. Clearcut and ade into a park The slopes either side of the shrine have also been clearcut in preparation of development.