There are wide ranges of blink response sensitivity in people. I never use red reduction because it does just the opposite of what I want, dark adapted irises instead of contracted pupils. I want their eyes wide and bright. There are a few things that help,one is to keep the ambient light low. and make sure no light source in on axis of the lens, which means no popup flash, or using shoe mounted flash if the subject is more than 15-20 feet away. Longer distances make the red reflection worse since the axis of the flash and the lens are closer spaced at a distance.
Some people have such fast blink response that the CLS communications flash triggers the blink. Maybe 1 in 50 people are so affected. The easy way to eliminate that is take a test show and read the settings the camera and flash used and set those for manual flash control and turn off CLS. Manual flash control and exposure is just better for any type of portraiture or group shots anyway. Being in manual mode also makes frame to frame exposure consistency better.
Light panels are becoming more popular for remote and studio shooting but the continuous light means light adapted pupils so used the absolute minimum light intensity and increase ISO to compensate.
Except when using a close ring light or beauty dish, lighting is usually off axis enough to not contract eyes or cause squinting. Outdoor, with high ambient light getting relaxed faces without eyebrow contraction or squinting is one of the biggest challenges. You have to the subjects to have shade in the eyes, a large screen defuser overhead to cast a filtered overhead or on-axis filter of the sun can lower the light level to get the open relaxed eyes that make the difference between a snap shot and a pro portrait. For it to be natural, expose for the bright background and use the flash, strobes or reflectors to bring up the fill light for proper subject exposure. Nikon SB- series flash units are really good in BL mode at balancing flash light to ambient light. Most users of the Nikon system do not realize how there are two independent metering systems when using Matrix metering with TTL flash. The flash has its own metering system but uses the same metering sensor in the camera for its calculations. The camera meters for the entire scene so a bright sky background will usually result in a face facing the camera will be far under exposed normally. The SB series flash with CLS uses the focus point for spot metering and sets exposure based on that spot, usually the eyes and ignores the background. So the person is exposed the same as the calculation for the background. It is the best flash control system in any brand camera. But with little experience you can do that yourself with any flash and any camera manually.
Another way to lower the odds of blink is use a slower shutter speed and use lower ISO, or smaller aperture, and switch the flash to rear curtain. The background will be exposed more but the dark subject only is exposed by the very short light burst at the end of the exposure. The subject is frozen and sharp and the background is exposed by the longer shutter for good color saturation and possible motion blur while the subject is crystal sharp exposed only by the flash at 1/1,000- 1/20,000 of a second depending on the flash and power setting.
So beware that red-eye are from too close converging lens and flash beams. Anti-red eye white light is undesirable because it light adapts the subject's eyes and the close down pupil and eyelids. Use off axis light either by flash triggers or a flash remote cord to move the flash away from the lens access. But doing that cast hard shadows that are usually blocked from view by the body when flash is close to the lens axis. The answer there is to not put subject against walls, mode them out from a wall and angle the flash to cast the shadow below and out of the frame. That is a big advantage of getting flash or strobes further from the camera and closer to the subject angled to cast shadows fully out of the frame to either or both sides.
With a small camera the easiest way to deal with that is hold the flash in the left hand and camera with the right hand and direct the light where it helps and away from where it doesn't. A larger camera and heavy lens makes that hard to shoot with one hand but I do it often with a D800 and 24-70 2.8 or 85 1.4/1.8 for hours at events. If it is a paid event you can have a lighting assistant with a pole mounted flash/softbox who can get the light right down on the subjects that wraps around them for very flattering light. That can speed up the shoot and lower your personal workload.
It does not have to be complex or expensive to get great lighting, a couple garage sale old manual flash, a shoe extension cable, or wireless controllers for $40 each, and any recent Nikon camera, lens combo....even kit lenses are capable of great images if you feed them good light, you do not need $2k portrait lenses, even for good bokah, just a bit of thought and common sense. A 100mm fl of a kit lens, even if max aperture is f/4.5 you can still get creamy backgrounds by simply positioning the subject a lot closer to you than the background.
If the background is cluttered and you want to isolate the subject, you have other choices other than creaming it out with f/1.4 lenses. You can use low key lighting almost anywhere to make the entire background disappear, thanks to the inverse square law that determines how quickly light falls off with distance. Simple, just set exposure so the background it so under exposed it is black....low ISO and narrow aperture and fast shutter speed or a combination based on preference. Then add flash close to the subject....instant studio with black backdrop. You can do the same, but not quite as easily with high key lighting by greatly overexposing the bright background so it blows out to white but have the subject in shadows so is properly exposed at settings the bright background is way over exposed.
All these things virtually eliminate blinks and red eye while creating studio like images with no or little additional equipment.
