There's very little reason to have glowing eyes in the visible spectrum. However, in the IR spectrum, we do see them:

The idea is that most IR cameras are not as sensitive as the human eye, so they need extra illumination to see anything. Putting the IR illumination right next to the camera proves to be very effective -- there are no shadows in the scene when you do this, so there's nowhere to hide.

This is practical in the IR spectrum but not the visible spectrum because humans would be very bothered by a bunch of white LEDs lighting up the scene from a camera. However, since they can't see infrared, they don't might a whole ton of IR illumination coming down.

In practice, some of the light from the IR leds is visible as a dull red glow, which shows up pink when photographed due to the way digital cameras process their images.

There's very little reason to have glowing eyes in the visible spectrum. However, in the IR spectrum, we do see them:

The idea is that most IR cameras are not as sensitive as the human eye, so they need extra illumination to see anything. Putting the IR illumination right next to the camera proves to be very effective -- there are no shadows in the scene when you do this, so there's nowhere to hide.

This is practical in the IR spectrum but not the visible spectrum because humans would be very bothered by a bunch of white LEDs lighting up the scene from a camera. However, since they can't see infrared, they don't mind a whole ton of IR illumination coming down.

In practice, some of the light from the IR leds is visible as a dull red glow, which shows up pink when photographed due to the way digital cameras process their images.