Interesting, but I was thinking of the possibility of the influence goin gin the other direction. Why strikes me is not any particular intetextuality, but simply the style and devices.
Here is an example passage from Book 3. This section is likely part of an original "pagan" passage that Jews later built upon:
And unto life-sustaining Phrygia
Straightway shall there a certain token be,
When Rhea's blood-stained race, in the great earth
Blooming perennial in impervious roots,
Shall, root and branch, in one night disappear
With a city, men and all, of the Earth-shaker
Poseidon; which place they shall sometime call
Dorylaeum, of dark ancient Phrygia,
Much-bewailed. Therefore shall that time be called
Earth-shaker; dens of earth shall he break up
And walls demolish. And not signs of good
But a beginning of evil shall be made;
The baneful violence of general war
Ye'll have, sons of Aeneas, Dative blood
Of Ilus from the soil. But afterwards
A spoil shalt thou become for greedy men.
O Ilium, I pity thee; for there shall bloom
In Sparta an Erinys very fair,
Ever-famed, noblest scion, and shall leave
On Asia and Europe a wide-spreading wave;
But to thee most of all she'll bear and cause
Wailings and toils and groans; but there shall be
Undying fame with those who are to come.
And there shall be an aged mortal then,
False writer and of doubtful native land;
And in his eyes the light shall fade away;
Large mind and verses measured with great skill
Shall he have and be blended with two names,
Shall call himself a Chian and shall write
Of Ilium, not truthfully, indeed,
But skillfully; for of my verse and meters
He will be master; for he first my books
Will open with his hands; but he himself
Will much embellish helmed chiefs of war,
Hector of Priam and Achilles, son
Of Peleus, and the others who have care
For warlike deeds. And also by their side
Will he make gods stand, empty-headed men,
False-writing every way. And it shall be
Glory the rather, widely spread, for them
To die at Ilium; but he himself
Shall also works of recompense receive.
Here is what I have written about this in the book I'm working on:
Let’s recall that all Sibylline works are really retrospective accounts of the past, which present themselves as ancient premonitions of the future. This section of the text is talking about tales of Troy. This passage starts off talking about earthquakes. Poseidon was considered by the ancient Greeks to be the god who controlled earthquakes. In the Homeric epics Poseidon is called the “earthquake-lord.” Dorylaeum was a town in the region of Phrygia that was noted for its natural hot baths. Dorylaeum was also frequented by earthquakes. Phrygia is an area in what is now western Turkey. Phrygia features in the epic stories of the Trojan War. According to the Homeric epics, King Priam married a Phrygian princess and the Phrygians allied with the Trojans against the Greeks in the war. Ilus is the legendary founder of Troy. The passage says that the Trojans will become a spoil of war, of course indicating that Troy will fall. The passage goes on to mention Erinys, which is another name for Helen of Sparta, who becomes known more widely as Helen of Troy. Helen is, of course, claimed to be the cause of the Trojan War.
So, this first part of the passage seems to be saying that the earthquakes from this region are indicative of its violence. This violence from Phrygia infects Troy and imbues itself upon the people of Troy. The passage then goes on to talk about Homer and the recording of the Homeric epics. The passage refers to Homer as the “aged mortal” who is a “false writer” and whose vision fades away. Homer is referred to as “a Chian,” which is a reference to the island of Chios, from which he supposedly hailed. That the Sibyl claimed Homer wrote falsehoods about the Trojan War is something that is widely attested to in the ancient literature.
For me, its just the overall style and the way that events and individuals from the past are alluded to, sometimes in semi-veiled terms. Of course this could just be calked up to a common style of all prophetic writings.
However, if it is the case, as the article that you linked proposes, that portions of Book 3 show similarities with Isaiah, then is it not possible that the same person who wrote Isaiah also wrote Book 3? Book 3 contains what appears to be a mix of older "pagan" material mixed with newer Jewish material.
What of this scenario? A Jew possesses the original "pagan" version of what is now Book 3. They read it and want to produce a similarly styled Jewish work. They produce Deutero-Isaiah, styled on the the Sibylline verses. At the same time, they decide to produce a Judaized version of the Sibylline work, producing significant portions of what is now Book 3 (and potentially Book 1). In this way, Isaiah is influenced by the original content preserved in Book 3 and also Book 3 contains new content that is shared with Isaiah.
Of course this is highly speculative and may be a bit too neat.