This is what Bruce Compton has to say about the neuter form of teleios. He is professor of biblical languages and exposition at Detroit Baptist Theological Seminary, so he should know a thing or two about NT Greek. I have also included his footnotes.
The Gender and Meaning of “the Perfect”
The critical question raised with these verses is the meaning of the term “the perfect” (to; tevleion) in 13:10. The term “the perfect” represents an articular neuter adjective functioning as a substantive and translated “the perfect” or “that which is perfect.”71 Much has been said about the neuter gender of the adjective and what that indicates in terms of the adjective’s antecedent.72 The best explanation is that the adjective gets its gender from the neuter noun forming the expression “in part” in 13:9–10. In other words, by using the neuter form of the adjective in this context, Paul signifies that whatever the “in part” refers to, “the perfect” refers to its counterpart or its antithesis.73 Having the adjective in the neuter gender thus links “the perfect” and the “in part” as having ultimately the same referent. Whatever the “in part” refers to, the “perfect” refers to as well. The only difference between the two expressions is the difference over the relative dimension or extent of the referent.
Having answered the question about the gender and antecedent of “the perfect,” what remains is to identify the meaning of “in part” in 13:9. Since Paul declares that the gifts mentioned in 13:9 are in some way “in part,” the proper approach to identifying the meaning of the phrase is to ask what these gifts have in common that could be described as “in part.” Based on the definitions given above, the common denominator among the gifts is that they all involve direct revelation from God. As such, the expression “in part” simply refers to the fact that the revelation communicated by these gifts is partial or piecemeal. The corresponding expression “the perfect” as the counterpart to the partial must refer to the full or complete revelation, of which these gifts contribute their portion. Finally, since these gifts are specifically identified in 12:27–28 as those which God has given to the church, the body of Christ, “the perfect” represents the full or complete revelation that God intends for the church. Thus, “the perfect” points to completed revelation God has intended for the church and has preserved in the New Testament.74
71 Similarly BDAG, s.v. “τέλειον,” p. 995. Carson inexplicably identifies the gender of the adjective as masculine (Showing the Spirit, p. 69).
72 Eg. Edgar, Miraculous Gifts, pp. 334-35.
73 The gender of an adjective is generally determined by the gender of the word it modifies. This is true even if the adjective is used as a substantive, as here. Mounce notes, "When an adjective functions as a substantive its... gender and number are determined by what it stands for" (William D. Mounce, Basics of Biblical Greek Grammar, 2nd ed. (Grand Rapids: Zondervan, 2003), p. 65). While the noun for which the adjective stands is not always clear or easy to supply, nevertheless that for which the adjective substitutes generally determines the gender of the adjective. See C. F. D. Moule, An Idiom-Book of New Testament Greek, 2nd ed. (Cambridge: Cambridge University Press, 1959), p. 96; Stanley E. Porter, Idioms of the Greek New Testament, 2nd ed. (Sheffield: Sheffield Academic Press, 1994), pp. 120–21; Wallace, Greek Grammar Beyond the Basics, p. 294. Porter emphasizes the exceptions where an antecedent noun is unnecessary or impossible to identify. On the relationship between ἐκ μέρους and τὸ τέλειον, see Theological Dictionary of the New Testament, s.v. “τέλειός," by G. Delling, 8:75. Discussing the use of the adjective in the New Testament, Delling states, "In the Pauline corpus the meaning 'whole’ is suggested at 1 C. 13:10 by the antithesis to ἐκ μέρους”
74 See, for example, Gromacki, who concludes, "Logically, to teleion must refer to completeness or perfection in the same realm as that referred to by to ek merous. Since to ek merous refers to the transmission of divine truth by revelation, the other term to teleion must refer to God's complete revelation of truth, the entire New Testament” (The Modern Tongues Movement, p. 126, citing Gilbert B. Weaver, "Tongues Shall Cease: 1 Corinthians 13:8," research paper, Grace Theological Seminary, 1964), p. 12).