Eye Gaze Biohead Eyes
 

I am wondering how to make eye .vzf files separate from the heads. Is that done in Peoplemaker or in 3dmenow? I'm trying to get an avatar's eyes to follow an object like in the "Follow that gaze" tutorial.

You would need to do that in your modeling program, in this case 3dmenow. I believe the sample vzf file in the tutorial you mentioned was created with 3dmenow, so it should be possible.