The first thing to do is make sure the white balance is where you want it.
"Brown" is a name we use to describe a shade of a very common hue. Just as we use "pink" when we want to specify a tint of the hue red ("tint" is a hue lightened; "shade" is a hue darkened), brown is dark orange. Orange and brown are the same hue. I recommend verifying this with paints -- it is one of the usually pleasurable parts of learning about color.
You will notice, though, that there is no orange preset in the Color Adjustment Brick, and no tints or shades either. The six hues that are there are simply presets arranged across the span of visible light that we perceive and color. Click any square (really, any one -- the order does not matter), then click the eyedropper and use it to sample the hue you want to adjust using the Color Adjustment Brick.
(Each Color Adjustment Brick allows six independent hue adjustments. You can see them all by clicking the "Switch to Expanded View" button {third in from the right, in the same row as the Action Menu}. You can have multiple Color Bricks for each Image.)
For eyes, you will likely want to zoom in, make the adjustment, zoom out to confirm it, and then click the Action Menu at the top right of the adjustment brick (the gear icon), select "Brush Color in" and apply it, using the brush, to just the eyes.
Also for eyes -- Léonies advice is excellent, in part because it is simpler than brushing in a Color Brick adjustment. You don't (most likely) care what the hue of the eyes is -- you want to enhance it regardless of the hue. The Saturation Quick Brush should do the trick. (Vibrancy, as I understand it, is essentially a saturation brush that features much less effect on orange hues*.) The standard trick for eyes (especially for wildlife photography) is to sharpen the eyeball and the eye lids. Use a light touch -- the effect should be present but not specifically noticable where it is applied.
(Added:)
(* The following is from the User Manual. Emphasis is mine.)
You use the Vibrancy Quick Brush adjustment to add saturation to desaturated colors only in the area of the image the adjustment is brushed on. Skin tones are not affected.
Message was edited by: Kirby Krieger