Can this be tracked back to some specific Evil Thing with glowing red eyes that predates film?
Yes, except the evil part, and not necessarily the color red.
If you have a cat, when you are in low light conditions you will see that their eyes are very reflective (this is part of what makes them able to see in the almost dark). This makes the cat nigh invisible except for its eyes. The concept of seeing eyes in the darkness (and registering that as a precursor to being attacked) can predate the period where humans became sedentary; when they still camped in the forest and thus were open to attack from nocturnal predators.
One of many resources online:
In the wild, an animal's eyes might be the first thing you see as they walk toward you in the dark. While your cat may be a domestic animal, they are no exception. This is because the glow in your cat's eyes derives its purpose from their wild ancestry.
The reason cats can see is because light reflects off objects into the cornea of their eye. [..] The main difference is that cats have an extra structure known as the tapetum lucidum. This is the part which creates the mysterious brightness they radiate at night, giving the cat's eye a glowing appearance.
This light is not new light emanating from the eye, but simply a reflection of any light which enters it in the first place. The membrane, however, can multiply this light up to fifty times. This is one of the reasons it can look so eerie when you see a cat's eyes seemingly glow in the dark. It is also why this is a common feature of nocturnal animals.
In conclusion, glowing eyes is a common feature of nocturnal animals. Therefore, anyone who is preyed upon by a nocturnal predator is going to be very afraid of seeing glowing eyes in the dark. Over a long enough period of time, this fear becomes a basic instinct, which is what happened for us humans. Our primate (or even reptilian) brains innately register this as a scary thing.
This is why it is scary to us humans, which leads to why it's used as a trope: because it evokes emotions in the viewer without costing much effort to film or create.