I've worked with GIMP for some things (eye glow effects, mainly) and I think this would also work there.
Myself, I mostly work with MS Paint, so the method I use when digitally drawing pony eyes is much simpler, if not as easy: "ellipse tool + steady hand with the brush tool" or sometimes just "steady hand with the brush tool".
I'm having trouble with the Pattern along Path method.. I don't have any kind of pattern like that and I'm completely new to Inkscape, so have been manually tapering all my lines. Are there videos for this method?
Depending on the pattern object you used, it might look like the line simply got thicker. However, there should actually a be a new object on top of the line which is a stretched/bent copy of the pattern object. Try dragging the "thicker" line and see if you actually have two objects there after applying the extension.
This is for Inkscape, a free, vector-based drawing program. As GIMP is to Photoshop, Inkscape is to Flash/Illustrator. [link]
I don't know what sort of clipping/masking capabilities GIMP or Photoshop have (since they're important for this method of making eyes), but the basic design principles should be applicable no matter what program you use.