I think there's a misunderstanding. I don't want to "see" the sidebands, I want to understand how they are created when mixing two signals together.
Edit: Whoops, just noticed the link. Reading it now.
Ok, that's interesting. According to the link:
That makes sense. However I think I'm failing to understand how changing the amplitude of the carrier creates two different frequencies in addition to the original two. It's just not "clicking" I guess.