What does the Chalcedonian Creed mean by person?

This question has to do with the mind and the will of Christ, in what has come to be known as "The Hypostatic Union". Comments below your question flag this up. From the link below, I would quote this summary about the Person of Christ: "The dual nature of Jesus Christ is such that Deity and humanity meet in one Person. The natures neither mingle, nor merge, nor 'switch'. They are two distinct things. They meet only in the Person of Jesus Christ. ...These two natures cannot 'merge' or 'mingle'. They are two different things. They unite only in the Person of Jesus Christ." https://hermeneutics.stackexchange.com/questions/66876/jesus-was-tempted-but-god-cannot-be-tempted-how-then-do-we-reconcile-james-1/66877#66877

In the link you provided [2.] The Center For Baptist Renewal explains what Chalcedon means by the person of Christ:

"...a selection from Chalcedon gives us guardrails:

one and the same Christ, Son, Lord, only begotten, to be acknowledged in two natures, inconfusedly, unchangeably, indivisibly, inseparably; the distinction of natures being by no means taken away by the union, but rather the property of each nature being preserved, and concurring in one Person and one Subsistence, not parted or divided into two persons, but one and the same Son, and only begotten, God the Word, the Lord Jesus Christ. . .

"According to Chalcedon, then, we must uphold the hypostatic union: Jesus is truly God and truly man, two natures united in one person, without any sacrifice of either nature or any blending of the natures. This helps us avoid classic heresies such as Apollinarianism (Jesus had a human body but a divine mind) and Nestorianism (Jesus was two persons with two loosely-connected natures), as well as modern kenoticism (Jesus surrendered certain divine attributes in order to live within the constraints of humanity in the incarnation). This also reminds us that there is one person or subject—namely, the Word made flesh (John 1)—who acts."

The Chalcedonian Creed included 'mind' in its understanding of 'person'. Chalcedon dealt with the two natures, which may be why you wonder if it denied Christ having a mind. It made no such denial. It did not answer all the questions, however, but it defined certain limits, to protect against heresy.

Chalcedon was in 451; Apollinaris was in the latter part of that century. He rejected the idea that Jesus possessed a human personality. This led to postulating a kind of divine or heavenly flesh of Christ; of two natures before the incarnation - divine and human - but only one afterwards. Later, Calvin and Reformed theology affirmed that only the human soul and body of Christ were born and suffered. Apollinaris said human flesh needs a spirit to direct and energize it, and now I quote from the scholar below:

"... in Christ this spirit is not that of a human nous, or 'intellect', but the Logos himself. Apollinaris equated the biblical concept of flesh with the Aristotelian view of matter, and the biblical concept of spirit with the Aristotelian view of form.

With Apollinaris there was no suggestion that Jesus was less than fully God, but the diminution of his humanity made it less than certain that we are his brethren and consequently his people... the countercharge of Apollinaris [was] that they really taught two Christs, one divine and one human.

A man who lacks a human intellect cannot truly be considered a man, as the fundamental element of his humanity, his human mind and the human will associated with it, is plainly lacking. By insisting that Christ's nous is "immutable," Apollinaris came into conflict with the Scripture, which speaks of him as growing in knowledge... The chief flaw in Apollinarianism is the fact that it seems to make the orthodox doctrine of salvation impossible...

The conviction that Jesus Christ has two complete natures, divine and human... was reaffirmed at Chalcedon." (Heresy and Orthodoxy in the History of the Church, pp.163-165 & last sentence from p.182, Harold O.J. Brown)

I cannot provide quotes from the ancient sources you seek, but I have tried to give details about what such ancient creeds incorporate in their use of the word 'Person', in light of how developing ideas wandered into unorthodox regions of thought, and how modern explanations seek to expose that with continuing orthodox views about the mind and will of the Person of Christ.