The San Francisco Peace Treaty was signed in September 1951 and Rhee Syngman drew the Rhee Syngman Line including Liancourt Rocks in the Korean territory in January 1952 before the treaty would be effective in April that year.
The main map of Korea didn't include either Ulleungdo or Liancourt Rocks, but you can see these islands in one of the seven additional maps, "Japan and Korea". [Click the left map to enlarge]
Ulleungdo was labelled as "ULLUNG (UTSURYO-TO)" and naturally painted in red, the same colour as Korea. Liancourt Rocks were labelled as "TAKE" and its colour is not clear - but at least it doesn't look in red when you used magnifying glass. And the name of the island was only labelled in Japanese name ("Take" of Takeshima), abbreviating "Shima" because "Shima"means island. This map seems to have adopted the same way to label Japanese islands, for example, Tanegashima was written as TANEGA, Yakushima was written as YAKU. So it is sure that the mapmaker believed that Liancourt Rocks belonged to Japan.
Takeshima/Dokdo was undoubtedly believed to be Japan's island before Rhee Syngman drew the line violating the international law.
[Broughton Bay was labelled as "Tongjoson Bay"]