Falloff materials, Light and Reflections for cartoon eyes

Even simple things can have good materials and Nodes are a small mess for me but Cycles is worth the learning curve! In experimenting with some unrealistic eyes, I saw that there’s a Node to make light falloff more rapid in a variety of ways for a given material. I’m interested in using that on an iris that is already concave and inside a Transparency/Gloss Mix sphere. I’d like the shadow to be more dramatic than the lighting provides in the scene without having to draw a gradient.

For that outer sphere with the Gloss material, I’d like to limit reflections by depth/distance and don’t know what Node might control that.

There’s a good observation by Blenderallday on another thread here that notes an eyeball reflection seems to add contrast and not be a perfect mirror of the scenery around it. Windows, skies and other high-key items far outweigh nearly all darks, interiors and such making the reflection more of a silhouette than a mirrored copy.

Attached shows iris shadow I’d like to intensify, reflection of Cube that the eyes are tracking I’d like to disappear by attenuation or some curve control that raises a reflection’s contrast - and that Blender file was experimental only. These orange eyes are all that remain - I’d start another file to continue work.