It turns out that characters with multiple pupils in their eyes are somewhat common in Irish literature (such characters sometimes appear in non-Irish works as well). However, the meaning of this varies between characters.

In some instances, having multiple pupils is a sign that the character has an "evil eye." For example, in the Togail Bruidne Da Derga (The Destruction of Da Derga's Hostel), a character with multiple pupils causes a juggler to drop his objects:

A man ungentle, huge, fearful, uncouth was Ingcél. A single eye in his head, as broad as an oxhide, as black as a chafer, with three pupils therein.

...

When he was swiftest, I beheld him at the feat, and as I looked, they uttered a cry about him and they were all on the house-floor. Then the Prince who is in the house said to the juggler: ‘We have come together since thou wast a little boy, and till to-night thy juggling never failed thee.’’ ‘Alas, alas, fair master Conaire, good cause have I. A keen, angry eye looked at me: a man with the third of a pupil which sees the going of the nine bands. Not much to him is that keen, wrathful sight! Battles are fought with it,’ saith he. ‘It should be known till doomsday that there is evil in front of the Hostel.’

(Online translation of The Destruction of Da Derga's Hostel)

However, in works like the Táin Bó Cúalnge, having multiple pupils can be a sign of beauty or supernatural sight (or both). To quote from this fantastic paper titled 'The Evil Eye' in early Irish literature and law (which is essentially the source for this entire answer):

The version that Ingcél has seven pupils in his eye has a parallel in descriptions of Cormac mac Airt and Cú Chulainn: they are said to have seven pupils in each eye. In both cases, this is explictly qualified as a sign of beauty. In Táin Bó Cúailnge Recension I, two of Cú Chulainn’s pupils are described as squinting, but the text supplies the comment that this was more an adornment than a disfigurement. The tradition of three pupils in Ingcél’s eye could be compared with another instance in Táin Bó Cúailnge Recension I: after the description of the poetess and prophetess Fedelm as a beautiful woman, it is said that she carries a weaver’s beam and has three pupils in each eye. There is no explanation offered of this characteristic: it could be a sign of beauty and it could be a sign of her supernatural sight. The latter is more probable, because the characteristic is separated from the description of her looks by the mention of the weaver’s beam. The weaver’s beam has been interpreted as a supernatural tool for prophesy. The triple pupils could, therefore, very well be a symbol of her clairvoyance.

(Borsje, Jacqueline; Kelly, Fergus: 'The evil eye' in early Irish literature and law.)

In summery, depending on the character and story, having multiple pupils is associated with (rarely) beauty, sharp site (i.e. clairvoyance), or destruction (i.e. "the evil eye"). However, I think you can connect those "symptoms" back to the evil eye; for example, being able to see the future/see well is one of the characteristics of having the evil eye, although in the Táin it's portrayed more positively.

If you're interested in learning more, I highly recommend that you take a look at the paper I cited about the evil eye: it's very interesting and connects the phenomenon to Irish law and a variety of non-Irish texts.