Ok so I got the cover off I'm not exactly sure what I'm supposed to be looking for so I just took a video of the inside of it to give you an idea.
OK, under the clutch, next to the plastic gear is the pawl and ratchet parts of the shift mechanism. I don't know why you are playing with the clutch. Shifting is a transmission problem. I would put the shift lever back on, and watch what is going on when you shift it. Have the bike on the center stand so that you can move the rear wheel back and forth so the gears can go into mesh...ARH