#braddourif

Starting with the ole one-eye highlight — they usually pick the right one, which is a little lifted and turned (I'm calling it his cat-eye):

Cue the lightning!!!

Sometimes it makes an iridescent crescent shape. I know it's meant to be scary, but he's such a terribly pretty boy:

Getting creative with some uplighting and a rare left eye (it's nice to see her getting some attention)...

...And some more extreme angles. How does this even work?!

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Contrast

Sometimes he pops them wide open, creating these huge, expressive magnets...

...Or squints lopsidedly...

...Or interrogates, challenges, threatens — alert but defensive, like a prey animal on the edge of lashing out.

He’s said he chooses roles that "turn him on" (pretty clearly in an artistic sense); many of these blend menace and vulnerability, and our boy dumps emotion into every. single. line. This can manifest as an intense, wary, combative look, with eyes wide under neutral or furrowed brows:

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Cry, baby

...And that's all before we mention the tears. He cries, of course, at will and liberally, and his eyes go red-rimmed and wet, highlighting them even more as he pins someone's soul to the wall with his gaze.

When he hovers right on the edge, they seem to shine in the dark.

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Bared

At times, his fair eyelashes almost vanish, compounding his unusual look with a birdlike or reptilian tinge.

Obviously, the shaved brows in LOTR add to this effect.

A couple more things you'll notice here: he'll hold his eyes wide open for much longer than normal, drawing out these moments and making him seem even more alien.

And when he gets up-close in someone's face (which is often), he's constantly switching his gaze between their eyes — totally fixated, as if scanning for emotional feedback. In my opinion, it adds to that vulnerability: to the object of his attention, he must seem like a predator freezing them in place... but it's also desperate, like a prey animal trying to decipher the other person's intent, all senses tuned to pick up their slightest signal. (Gríma Wormtongue and Jack Dante especially have this pathetic air about them: grasping at sources of warmth while lashing out at the harsh, unintelligible world around them, allying themselves with uncontrollable destructive forces in an attempt to establish a place for themselves........)

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TL;DR

The eyes — and how he uses them — are the standout scrungly feature, the main reason we can’t look away from this unforgettable weirdo.

The cat-eye asymmetry pulls focus;

His ice-blue irises are light traps, framed in textured shadow;

His full-bore emotional commitment ramps up the anguish and torment to an aching crescendo that's impossible to ignore.

Eventually I'll follow up on other contributing factors, but for now, I'll leave you with a couple of article snippets about The Eyes:

Imagi-Movies: Vol 1 No 2 — Winter 1993/94. Pages 11-13: "Traumatic - Brad Dourif". Link

SoHo News: November-December 1981. "Tension and mercy - Brad Dourif glowers for our sins" (an article all about his eyes! But they don't mention the asymmetry.)

[Gifs were mostly stolen from the GOAT, @exdeputysonso — with some of my own, mostly the square ones. Shout-out to @dragonsbloodsnowcone for inspiring this word vomit.]