Do you know of any Atheists who are convinced of Christ's righteousness?
You're misapplying that word meaning. It simply means to show somebody something. Here.
Theological Dictionary of the New Testament
ἐλέγχω (elénchō)
2. In the NT the use is restricted. With the accusative of person it means “to show people their sins and summon them to repentance,” either privately (Mt. 18:15) or congregationally (1 Tim. 5:20). The Holy Spirit does this (Jn. 16:8), as also Christ does both now (Rev. 3:19) and at the parousia (Jude 15). No one can do it to Jesus himself (Jn. 8:46). Sinners experience this exposure when faced by the prophetic call (Lk. 3:19), divine instruction (Heb. 12:5), or the law (Jms. 2:9). perí is used to denote the fault (Lk. 3:19), with hóti for elaboration (Jn. 16:9ff.). Correction as well as exposure or conviction is implied; the corresponding action is élenxis (2 Pet. 2:16) or elegmós (2 Tim. 3:16).
Greek-English Lexicon of the New Testament: Based on Semantic Domains
33.417 ἐλέγχω; ἔλεγξις, εως f; ἐλεγμός, οῦ m: to state that someone has done wrong, with the implication that there is adequate proof of such wrongdoing—‘to rebuke, to reproach, rebuke, reproach.’
ἐλέγχω: ὁ δὲ Ηρῴδης ὁ τετραάρχης, ἐλεγχόμενος υ’π̓ αυ’τοῦ περὶ Ηρῳδιάδος ‘Herod the tetrarch was rebuked by him because of Herodias’ Lk 3:19; μᾶλλον δὲ καὶ ἐλέγχετε ‘but rather rebuke them’ Eph 5:11.
ἔλεγξις: ὃς μισθὸν ἀδικίας ἠγάπησεν ἔλεγξιν δὲ ἔσχεν ἰδίας παρανομίας ‘who loved the money he would get for doing wrong and was reproached for his transgression’ 2 Pe 2:15–16.
ἐλεγμός: πᾶσα γραφὴ θεόπνευστος καὶ ὠφέλιμος πρὸς διδασκαλίαν, πρὸς ἐλεγμόν ‘all Scripture is inspired by God and is useful for teaching, for rebuking’ 2 Tm 3:16.
A Concise Greek-English Dictionary of the New Testament
ἐλέγχω (aor. pass. ἠλέγχθην ) show (someone his) fault or error, convince (someone) of (his) fault or error; show (something) up for what it is; prove guilty, condemn; rebuke, reprove
Synonyms of the New Testament, 9th ed.
... ἐλέγχειν is a much more pregnant word; it is so to rebuke another, with such effectual wielding of the victorious arms of the truth, as to bring him, if not always to a confession, yet at least to a conviction, of his sin (Job 5:17; Prov. 19:25), just as in juristic Greek, ἐλέγχειν is not merely to reply to, but to refute, an opponent.
... ἔλεγχος implies not merely the charge, but the truth of the charge, and further the manifestation of the truth of the charge; nay more than all this, very often also the acknowledgment, if not outward, yet inward, of its truth on the part of the accused; it being the glorious prerogative of the truth in its highest operation not merely to assert itself, and to silence the adversary, but to silence him by convincing him of his error.
Vine’s Complete Expository Dictionary of Old and New Testament Words
CONVICT (including the KJV, “convince”)
1. elencho (ἐλέγχω, 1651) signifies (a) “to convict, confute, refute,” usually with the suggestion of putting the convicted person to shame; see Matt. 18:15, where more than telling the offender his fault is in view; it is used of “convicting” of sin, John 8:46; 16:8; gainsayers in regard to the faith, Titus 1:9; transgressors of the Law, Jas. 2:9; some texts have the verb in John 8:9; (b) “to reprove,” 1 Cor. 14:24, RV (for KJV, “convince”), for the unbeliever is there viewed as being reproved for, or “convicted” of, his sinful state; so in Luke 3:19; it is used of reproving works, John 3:20; Eph. 5:11, 13; 1 Tim. 5:20; 2 Tim. 4:2; Titus 1:13; 2:15; all these speak of reproof by word of mouth. In Heb. 12:5 and Rev. 3:19, the word is used of reproving by action. See FAULT, REBUKE, REPROVE.
