I got a Naki Touring Wheel without any packaging or manual. It doesn't even have a name and printed on the base is "Steering Wheel for PS," which implies it came out before the PS2 did. I'm pretty sure it is a Touring Wheel as it looks exactly the same except it has a red rather than a blue trim. No foot pedals, hand pedals only. If anyone knows its true name, I would love to know what it is. By the way the wheel looks like the Naki N4 Mini Racing Wheel, but the base is fixed and wide rather than detachable and narrow.
The wheel has a Mode button that can switch on the fly from Digital Left/Right, Steering Wheel, Analog Left/Right, and nothing. Button configurations are also different so you need to hit Mode while in the control setting of the Option menus to see what the changes are and to edit them as needed.
Anyway here are its compatibility:
GT1 - on PS1 yes (force feedback on Digital and Analog only), on PS2 no.
GT2 - on PS1 yes (force feedback on Digital and Analog only), on PS2 yes but no force feedback and connection using the Mode button is flaky. You need to select the mode you want and then restart the PS2. Otherwise the PS2 will think the wheel is disconnecting itself all the time and bring up the pause menu repeatedly. That is a good indication it is a PS1 and not a PS2 wheel (although later Naki wheels are for both PS2 and PS1 according to their packaging).
GT3 - yes, but no force feedback and only 2 Modes (Digital and Analog).
GT4 - yes, but no force feedback and only 1 Mode (Analog).