An unfortunate side-effect of using flash is the so-called steel-eye effect (more generally known among naturalists and wildlife photographers as eye shine) that sometimes occurs.  As explained in section 4.3.3, the incidence of steel eye can be reduced by raising the level of the flash above your camera’s lens (though this can be a distance-dependent remedy, as explained below).  Raising the flash creates other problems, however: the flash may be more unwieldy to carry in the field (not to mention more fragile, due to the additional mounting hardware and cables required), and aiming the flash precisely at the subject becomes more difficult since the light path of the flash becomes more oblique to the imaging light path of your lens.  Fortunately, most cases of steel-eye can be fixed fairly easily in Photoshop, rendering the use of off-shoe flash brackets less critical.
    Consider the example image below.  On the left is the raw image.  The large gray disk in the bird’s eye corresponds to the bird’s pupil; the gray appears because the light from the flash is passing through the bird's pupil and striking the highly reflective layer of cells in the bird’s retina (at the back of the eyeball), called the tapetum lucidum.  By moving your flash unit further from your lens (in any direction—but usually upward), at close distances the angle of the flash's light rays will keep those rays from reflecting back in the direction of the camera once they’ve entered the bird’s pupil.  At longer distances you may need to move the flash unit progressively further from the lens (e.g., elevate the flash bracket even more) to achieve the same angle as measured at the bird’s eye, since that angle is distance-dependent¹. 



    Note in the above image (on the left) that in addition to the gray disk there are two tiny points of light, one at the center of the bird’s eye (within the disk) and one at the 11 o’clock position at the perimeter of the eye.  These points of light are reflections from the bird’s cornea, which is on the front (outside) of the eyeball; thus, these originate from a different anatomical part of the bird’s eye.  The bright dot in the center of the eye is a point reflection of the flash.  However, the white dot in the upper left is actually a catchlight (also known as a specular highlight)—a point reflection from the sun.  Catchlights (from the sun) are natural, and in fact are desirable with black-eyed birds, because without a catchlight the eyes look dead.  In the right pane of the above figure we’ve eliminated both the steel-eye and the two points of light, by painting over them with a black brush, and then added a smaller, rudimentary catchlight in the 1 o’clock position using a white pencil tool.  In this case we could have left the original catchlight that was present in the 11 o’clock position, but its proximity to the outer edge of the eyeball was slightly distracting, so a new one was drawn elsewhere.  In the rest of this section we’ll explore methods for creating and positioning catchlights in birds’ eyes.  Note that birds with non-black eyes typically don’t need a catchlight, because the contrast between the pupil and the iris usually gives the eye sufficient detail to avoid looking dead or artificial.  Removing a catchlight from a non-black eye can be done either using a brush of the appropriate color, or using the clone tool (section 11.5).
    The figure below shows a random sample of natural catchlights taken from bird photographs in which flash was not used (i.e., these are natural reflections of sunlight, and would be visible to you even if you were just looking at the bird through binoculars or with the naked eye).  There are several generalizations we can draw from these examples.  First, they mostly range from the 10 o’clock to the 2 o’clock positions (with a few exceptions).  This is because the sun is usually above the bird, so its reflection will generally be in the upper half of the bird’s eye. 



Second, the catchlight tends to be a concentrated point of white, though it can also appear as a more diffuse gray area (e.g., eyes #7, #8, #9, #19 in the above figure).  These latter diffuse patterns tend to occur when the sky is very bright but the sun itself is not directly visible in the sky (as on days with a thin white layer of clouds in front of the sun).  In extreme cases, you can see (if you zoom in on a RAW file) a detailed reflection of the horizon (e.g., eye #9 above).
    When the bird’s eye already shows a natural catchlight, in most cases you’ll probably want to simply leave it as-is.  If there’s any steel-eye or flash reflection on the cornea, and if you can remove those artifacts without also removing the catchlight (i.e., by painting over them with a black brush, while being careful not to paint over the catchlight or even to disturb the subtle corona or gradient that may be present around the catchlight), then that’s usually desirable.  In cases in which there is no catchlight, or in which you have to eliminate the catchlight in order to also eliminate any steel-eye, you’ll want to draw in an artificial catchlight afterward.  In order to learn how to do that, it’s useful to take a detailed look at some natural catchlights at the pixel level.  For this purpose, in the figure below we’ve enlarged the eyes from the previous figure, to reveal the individual pixels making up the image.



    Notice that in many cases the catchlight consists of one or two bright pixels flanked by some number of darker pixels.  Often those flanking, darker pixels spread outward from the bright center in a strictly horizontal or vertical direction.  Imitating this type of catchlight is quite easy in Photoshop, using the Pencil tool: 


In the image below we show such an artificial catchlight.  On the left is the zoomed-in view, which shows that we’ve drawn a single white pixel and then two darker pixels next to it.  The right pane shows the effect when viewed at 100%.



    Note that you’ll usually have to experiment with different brightnesses when drawing the catchlight with the pencil tool.  You can do this one of two ways.  First, you can change the pencil color from pure white to a shade of gray and then re-draw it in the same position.  This can become tedious after doing it many times.  Another option is to simply draw it once using the brightest shades (i.e., pure white for the main point and half-gray for the two flanking points), and then select the eye using the Quick Select tool and use the Levels tool to darken the catchlight until it looks good to you.
    Larger catchlights can in theory be drawn using the Brush tool (with a soft-edged brush) rather than the Pencil tool, though it can be difficult to make this work convincingly in practice.  If you’re especially good at digital painting and/or you have the patience and creative bent, you might try creating one of the more diffuse types of catchlights as exemplified above (e.g., #7, #8, #9 in Figure 11.4.3).  Doing so requires that you keep in mind the implied curvature of the eye when you paint in the diffuse shape.  Note that you’ll probably want to do your painting when zoomed in quite far, so you can see the individual pixels (to make sure you’re not painting over those pixels that border the eye); however, you’ll almost certainly want to assess the aesthetic effect on the zoomed-out (100%) view. 
    Another option worth considering is to clone a catchlight from another of your photos, using the Clone tool (section 11.5), or by copying the catchlight from one image and pasting it as a new layer in the other image.  In a similar way, if you don’t like the position of a natural catchlight, you can copy it to a separate layer (of the same image), paint over the original catchlight with a black brush, and then use the Move tool to drag the catchlight around to different positions in the eye, until you find a position that looks best to you.  A particularly convenient way of doing this is to use the arrow keys on your keyboard to move the catchlight layer by tiny increments in any direction, so you can assess the visual impact of these small changes without the mouse cursor being in the way.  Note that you’ll also want to turn off the “Show transform controls” checkbox in the Move tool’s parameter panel, to avoid distraction.
    Finding the ideal position for a catchlight is not always easy.  Ideally, you need to know the location of the sun, relative to the scene.  This can often be deduced by observing the directions of shadows in the photo.  Once you know the location of the sun relative to the locations of the bird and the camera, you can deduce (roughly) the angle at which rays of sunlight strike the bird’s eye.  Recall from elementary physics that the law of specular reflection states that in the case of a planar mirror, the angle of incidence equals the angle of reflection.  For a spherical object such as a bird’s eyeball, this law can be applied by considering a plane tangent to the sphere, as illustrated in Part A of the figure below.



In Part B of the figure above we consider the point of reflection on the surface of a sphere for the sun at different angles relative to the sphere and the camera.  The white dot represents the specular highlight that would be perceived on the surface of the sphere from the perspective of the camera at left.  Thus, with the sun directly over the bird, the catchlight would appear quite high in the visible portion of the bird’s eye, whereas with the sun at a lower elevation (or behind the camera), the catchlight would appear lower in the eye.
    Obviously, you don’t kneed to compute angles and perform precise ray tracing in order to find the ideal location for an artificial catchlight in a bird photo.  In practice, you can follow your intuition by trying various locations for the catchlight and taking note when your visual instincts respond favorably to what they’re seeing.  The primitive parts of your animal brain are surprisingly good at alerting the rest of your psyche to things that look unnatural (or, conversely, things that look especially attractive).  Much of the art of digital postprocessing—perhaps far more than you realize—is about learning to listen to that part of your brain and trust in your instincts.

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¹Think about what happens to an isoceles triangle when you stretch the triangle to make it taller: the angle of the apex decreases.  In the limit, this angle will approach zero, and the two sides of the triangle will therefore tend increasingly toward becoming parallel.