This unnamed island is located on Earth, about half-an hour by boat from the Eastern Capital, and serves as the home of Tokunoshin Ōmori. It is a small island, dense with vegetation, which contains Ōmori's home, docks, and his laboratory. It was previously terrorized by a monster shark until it was later killed by Jaco.
Sometime prior to the start of the Jaco the Galactic Patrolman, the island served as the host of a research project, funded by the government, in the hopes of learning the secrets of time travel. Hired as the chief supervisor to the project, Ōmori moved to the island along with his wife. At some point after this, an assistant managing the high-pressure gas made a mistake and caused a terrible accident which killed many people, including Ōmori's wife. After the accident, the research lab and the government abandoned the time machine project and the island. However, Ōmori refused to leave the island due to his wife being buried there. Ōmori would then continue attempting to make the time machine work for sometime afterwords.
Later on in life, Tights has taken up temporary or permanent residence on the island. She's refurbished Ōmori's old home, hanging up pictures of Jaco and the like. Additionally, the island itself appears to have been reclaimed from nature, with much of the excess foliage being removed. Whether she lives alone or with Ōmori himself is unknown.