Red-eye-reduction is a setting that creates a double flash or blinking flash right before taking the real photo. The red in the photo is actually the back of the eyeball reflecting that flash back to the camera.
I hate red-eye-reduction.
For a couple of reasons...
1. It doesn't always work
What happens is all the extra flashes from your camera are meant to make the human iris close smaller, reducing the reflection from the back of the eyeball back to your camera. Or in some cameras the flash that precedes the photo, detects the red, then tries to fix it digitally. Some do ok.
2. It wastes battery
All those extra flashes are taking a toll on your battery
3. It takes to long to take the photo
After waiting for all the extra flashes the moment is lost. Oh well, try again next time, then the flashes take to long again.
So, turn off red-eye-reduction. Every camera that has red-eye-reduction, can turn it off. Read your manual, and it will tell you how to disable it.
1. Don't use a flash.
Just to reiterate, the red-eye comes from the reflection of the camera flash off the back of the eyeball.
Or if you must use a flash
2 . Have your subject look anywhere but directly at the camera.
This will not allow the reflection from the back of the eyeball to reach the camera.