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Evaluate what each light did effectively or not:
Key light: It modeled the face nicely putting highlights in natural looking locations (i.e. same place downward light does)
Kicker right: It helps to model the side of the cheek but also highlights the ear which is closer. Highlights attract attention on a dark background. Do you want the viewer dwelling on her eyes and mouth or distracted of them by the brighter highlights on her ear?
Kicker left: Same cause and effect attraction/distraction on side of the face and far ear, and light angle relative to face caused it to sneek through the > notch of the far eye and create a "rogue" highlight on the tip of her nose — the brightest one on the face.
Fill? The missing ingredient here is frontal chin level fill. Note the very dark teeth and dark shadow under lower lip? The key light position was highlighting most of the front of the face with no need for fill there, but was shaded from the mouth. A chin level fill source just under the lens (assuming it is raised over the eye line) will illuminate the mouth and teeth. I use a 22" dish for fill it creates a wide footprint w. generous "spill fill" effect off ceiling and walls similar to the wrap-around fill of skylight.
Thinking in terms of goals of where on the face you want the viewer to dwell in in a portrait the eyes and mouth are the main focal points. Compared to the them the nose and ears are distractions. Those goals should inform the overall lighting strategy for the face to draw attention to the eyes and mouth and keep the viewer focused there and not distracted by or consciously aware of ears and nose. You don't want thoughts about the nose or ears to enter the viewer's mind because it will usually be some negative thought about their size and appearance.
Lighting strategies differ in terms of cause and effect on light and dark backgrounds.
On a dark background highlights are like eye mangets attracting the eye there. Shaded areas blend into the backgorund and don't get noticed as much. So if the goal is to attract maximum attention the eyes and mouth and hold it there on a dark background you'd logically want to highlight the front plane of the face and put the ears you don't want noticed into the shadows; like the star of a show in the spotlight on a dark stage. So on a dark background putting brighter highlights on the side of the face and ears is counter productive, again assuming the goal is max. "hang time" on the front of the face. If used to nuance the shape of the cheekbones keeping the intensity of the kickers lower than the key light will keep the side of the face darker than the front and create the desired modeling with the eye catching and distracting glare.
As mentioned the background changes some aspects of the lighting strategy because if the goal is to contrast the front of the face. If the background was white the bright glaring kickers would made the brighter sides of the face blend in and disappear into the background. Perceptually that has a similar effect as highlighting the face on a dark one, the front side of the face the camera sees seems to be slimmer because the brain focuses more on what contrasts with the background the most. So on a white background a full face (nose directly at camera) pose with centered key light, chin level centered fill and two "hot" kickers on either side creates a front plane of the face which is warm in color (good color contrast) with the kickers making it appear slimmer because the sides blend into the background at the brain tends to "tune them out" on when concentrating on the eyes and well lit mouth and smile.
To create a similar "more attention on the front of the face" dynamic on a dark background you need to understand what centered fill does on a cause-effect level. It's not "flat" fill because a head is a 3D object. What is closer to the fill (the nose) will be illuminated more, what is further away (the ears) less. That creates the ideal gradient on a face for a portrait on a darker background if the goal is attention on eyes and mouth. The nose shadow (if seen by camera) winds up being the most filled, lightest and least distracting. The fill falls off over the cheekbones creating the "wrap" gradient as it fades in intensity with distance and the ears wind up significantly darker (if not hit with key light or kicker) and will fade into the background and not be noticed much if at all. Net effect perceptually? Attention of the viewer stays on the front of the face.
The take-away advice? Before creating a highlight on a face with light source (key or kicker) consider how it will attract the eye of the viewer on the background being used. With the highlighted area CONTRAST or blend into the background. After creating the highlights and analyzing where they attract attention look critically at the shadows. Where are they darkest and lightest on the face? Unfilled areas such as under the lip and teeth here indicate a lack of fill which most be addressed by positioning fill where it can reach those areas. Chin level or slightly above fill source, centered, will fill most areas the camera sees. If using fill below chin level (i.e., clamshell) take care the fill does not create shadows on the top of the cheekbones (opposite of natural fill).
Once you are aware of the cause and effect you will be more consciously aware of what each light hits and how it attracts and spot problems like the highlighted tip of the nose, dark teeth, etc. You can create a pattern similar to this, but without the imperfections by toning down the kickers (or just adding reflectiors on the side to nuance the shaded sides) and getting fill on the front of the face as the foundation for the lighting pattern. Try it and compare results.
Before setting lights consider facial angle to camera and symmetry of the features. Here the ears are unequal. It's not a balanced full face — nose at camera equal size ears — nor is it a "clean" oblique view where the far ear is hidden. Posing the face to the camera for symmetry of appearance with precise angles is usually more flattering than bits of ear sticking out and the two ears winding up looking different. Show both equally or hide one completely.