All the white gears do on any system is raise or lower the distance from the CDVD-ROM Disc and the LASER head. They have nothing to do with one being for a PSX game and another being for a PS2 game.
After I read the steps below, Its actually not that hard.
The procedure is the same. Just try starting both gears at the same point, and gradually move each gear (equally) 4 or 5 clicks between each test. ONLY if this does not work, then you must take out the laser unit from the CD tray, (which is easier than you'd think). Flip the laser unit over after you've pulled it out, and there will be two capacitor trimmers labeled "CD" and "DVD". Before you turn either of these, mark each one with a fine point pen with lines to indicate their original positions. In your case, you should only have to adjust the one that says "DVD". Turn it with a small screw driver ever so slightly, (approximately 5 thousandths at a time or so,) put the system back together enough to test a PS2 disc, and repeat if necessary.
Source: http://mattread.com/blog/2004/01/ps2-disc-read-error-fix
Hope this helps!