Two things, first you need an eye light if its not a modeling light for the flash, than you need a real eyelight just to dilate the pupil, it need not and in fact should not effect the image at all, I use these little LED mini superbright flashlights, I put a picture below, the blue is from qvc, 3 for $20.00 with batteries (each uses 3 AAA's) the black is brighter and from national liquidators for 1.99 no batteries, also uses 3 AAA's they are almost uncomfortable to shine in the eyes, and very blue (8000-12000 degrees kelvin) they seem too bright, they are not that bright in reality, but in small spaces I sometimes place a piece of diffusion (frost) cut into a tiny circle to fit in front to turn them down a bit because when I am close and they are close to the model they are annoyingly bright to shine in the eyes of someone. At 5 feet they give you about f 2.8 at 1/5th of a second at 100 iso which is nothing, but when its in your eyes from 7 feet its almost blinding you. They work great, 4 inches long, have 9-12 leds and the led's are so efficient that they last for a very, very, very long time on 3 AAA's, they will likely be stolen before they need to be replaced and the lights will last about 100,000 hours and most are decently waterproof. you can mount them to an elastic strap and velcro closure and that can wrap around your lens, or on a bracket, in your hand, or around the radio slave. You can also have it on a stand or an assistant aiming it, but I find anything that relies on a stand or person is not likely to be where I want it when I want it and how I want it, its easier to have it aimed like the lens is so if I see the eyes they are lit.
Now if your using hotlights or in daylight this is not needed. This often helps reduce and often eliminates red eye when using a ringflash without a modeling light, or any on camera flash.
Now basically if its a lit face thats all that is needed to get bright eyes to glow, it allows the pupils to be constricted and the color very apparent. If the face is not lit by the strobe they will never glow unless you want to try to use a focused light to spot each one which I can assure you is not what your seeing in most shots. Eyelights
twinkles for the eye in film
Hope that helps. Of course there are many lights that can be used, but these are so damn good at it and cheap that its hard to beat and the size is perfect.
And yes on a very, very rare occasion, we use an extra eyelight for the models that is strobe, its more a face light, they have a few tiny softbox like setups that are about 7x7inch they often connect to a little slave light, and are almost a snoot type size, they are generally powered 1 stop under the main and just pops the face a bit, but its more for static beauty shots and does not sound like what the question was referring too.
