Below is a Japanese map of Ulleungdo called the 鬱陵島図 and was made by the Office of the Governors-General of Korea (朝鮮総督府) in 1918. The map shows the island in a great deal of detail, including not only Jukdo (竹島), Gwaneumdo (觀音島), and the more well known rock islets (石島) around Ulleungdo, but also the lesser-known rocks and even the small rocks near the shore line. (You can see a Japanese language post mentioning the map HERE.)
There are two things about the map that I find especially interesting. One is that it shows two fairly large rocks south of Jukdo, just off the east shore of Ulleungdo. One of the rocks is labeled 胄島 (Judo), with the name "北苧岩" in parentheses. Judo (胄島) means "Helmet Island" and may have been the Japanese name for the islet since there is no Japanese pronunciation guide written above the name. At any rate, this is evidence that even rocks were referred to as "islands." By the way, there is a rock off the northern shore that is labeled as an "island": 一本立島 (竹岩).
The second thing about the map that interests me is the name of the peak on the southern tip of the island. The peak is labeled as 可頭峰 (가두봉 - Gadu Peak), which I think translates as "Seal Head Peak." Koreans used to refer to the sea lions on Ulleungdo as "Gaji-eo" (可支魚), of which the first character is the same as the first character in the name of the peak. Old Western maps also labeled that part of the island as "Seal Point." If you look closely at the map, you should notice a small islet just offshore of "Seal Point." Modern Korean maps show the name of this rock as "Gajae Bawui" (가재바위), which means "Sea Lion Rock" (可支岩) in the Ulleungdo dialect. (See the second map below.)
I think it is very likely that "Sea Lion Rock" was the place referred to as "Gajido" (可支島) in a 1794 Korean survey report of Ulleungdo since "Gajido" means "Sea Lion Island" and since rocks were also referred to as islands. "Geobuk Bawui" (거북바위 - Turtle Rock), on the southwest coast of the island, could have also been Gajido since it is very close to a seashore cave that was labeled as "Gaji Cave" (可支窟 - Sea Lion Cave) on Lee Gyu-won's 1882 map of Ulleungdo. Today, the cave is called "Gajae Cave" (가재굴), which again means "Sea Lion Cave" in the Ulleungdo dialect. Koreans claim that Gajido was another old Korean name for "Dokdo" (Liancourt Rocks), but they have no maps or documents to support that claim. Besides, since Gajido was mentioned in a survey report of Ulleungdo, not Liancourt Rocks, it is almost certain that it was just one of Ulleungdo's neighboring rock islets.