I actually fired up GT1 last night and checked.
After you have won all your "red dots" indicating races won in all classes on all tracks in difficult mode, "HiRes GT" appears in the bottom slot of the "Bonus Items" page. It is a selectable item, and works just like Arcade time trial mode, with normal Arcade car selection, but the only tracks available are Hi-Res versions of CR5, SSR5 and SSR11. As with the main Arcade Time Trial mode, the top 8 times are recorded, along with with a three-letter player name.
I must not have played it much in this, my "original game". On my second attempt with a WRX'96STiIII I beat all three other recorded attempts with that car, and was in 4th, about 10 seconds behind my Viper time. And I had made several visible total gaffs during the run.