Well, seems like the church follows eye "physical eyes" teaching at least somewhat, what with their watchmen having those eye-covered lanterns of magical doom.
Not the lanterns only get covered in eyes after the Pale Blood Moon appears, or if
you get enough Insight, so it's most likely Eldritch Bullshit rather than the Healing Church covering them in eyes.
As for the Line your Brain with Eyes bit, I see it as both metaphorical and literal eyes on the inside.
See, as you gain more Insight, you begin to understand and perceive all the eldritch bullshit going on around you, much like Lovecraft protagonists go mad not simply because they saw some huge blob covered in mouths and eyes, but because the simple fact that blob
exists is enough to get them to question what other things in the ancient books and stories is real, to get them to question the very foundations of what they think is reality.
Insight is Knowledge and Understanding. As we see with the lore surrounding the Cleric Beast's and Vicar Amelia, the people who woupd have the most Insight, the clerics of the Healing Church, turn into the most hideous and strongest Beasts, suggesting an actual connection between the Mutations and how much Insight you have, as if this understanding guides the changes.
Therefore, I think it's possible that as you gain Insight, you may actually mutate a bit and get Eyes growing out of your brain, Brain of Mensis style, especially if you believe the Line you Brain with Eyes part is Literal.
The many eyes in a jar inside Byrgenwerth and the fact the brainsucker dudes eat your insight by sticking a tentacle on your brain might also be evidence to support this theory.
And of course, I might be completely wrong.