Unfortunately I don't know enough Hebrew to settle your question linguistically.
Nor do I have any confidence that I understand Genesis 1 enough to provide a complete, coherent explanation for why this portrait of the origin of the sky-land system was the ideal setup for all that follows. It mostly seems to involve the order in which things were made which, from a scientific perspective is patently wrong.
"Rule the day?" "Rule the night?" I don't have that figured out. I do know that we are told that in the night, working is completely impractical:
[Jhn 9:4 KJV] (4) I must work the works of him that sent me, while it is day: the night cometh, when no man can work.
Which reminds us that this passage is much more about spiritual truths.
The separation of the light into light and dark seems to precede the making of the sun and moon by three days so it could be argued that neither "light" was the generator of the light!
I also don't think that referring to the moon as a second "light" is necessarily incompatible with the moon being a reflector of the sun's light. I mean, we modern people have no trouble talking about "Clair de lune" (French for "light of the moon", "moonlight").
There is strong evidence that the ancients, from earliest times knew that the moon reflected the sun and a great deal of other astronomical matters.
Many translators into English render Hebrews 1:3a as "He is the radiance of the glory of God", such as:
[Heb 1:3a ESV]
He is the radiance of the glory of God
and the exact imprint of his nature,
and he upholds the universe by the word of his power...
While others translate it as "the reflection of":
[Heb 1:3a ISV]
He is the reflection of God's glory and the exact likeness of his being, and he holds everything together by his powerful word. After he had provided a cleansing from sins, he sat down at the right hand of the Highest Majesty
The word in question is this:
ἀπαύγασμα, ατος, τό (s. αὐγάζω; Heliod. 5, 27, 4 φωτὸς ἀ.; TestAbr A 16 p. 97, 17 [Stone p. 42]; Philo; Wsd 7:26; Tat. 15, 3 τῆς … ὕλης καὶ πονηρίας [of hostile spirits]; Plut. has ἀπαυγασμός Mor. 83d and 934d; PGM 4, 1130 καταύγασμα) act. radiance, effulgence, in the sense of brightness from a source; pass., reflection, i.e. brightness shining back. The mng. cannot always be determined w. certainty. The pass. is prob. to be preferred in Plut. The act. seems preferable for Wsd and Philo (Op. Mundi 146, Spec. Leg. 4, 123, Plant. 50), corresp. to Hesychius: ἀ.=ἡλίου φέγγος. Philo uses the word of the relation of the Logos to God. Christ is described as ἀ. τῆς δόξης radiance of his glory Hb 1:3 (the act. mng. in the Gk. fathers Orig.; Gregory of Nyssa; Theodoret; Chrysostom: φῶς ἐκ φωτός. Likew. Theodore of Mopsu.; Severian of Gabala; Gennadius of Constantinople: KStaab, Pauluskommentare ’33, 201; 346; 421). For this ἀ. τῆς μεγαλωσύνης 1 Cl 36:2.—FDölger, Ac I 1929, 269ff. DELG s.v. αὐγή.
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed.). Chicago: University of Chicago Press.
Exported from Logos Bible Software, 9:26 PM April 13, 2019.
Etymologically the word has the sense of "light from/off something else" leading scholars looking to context and trying to determine if a given usage is intended to mean "the radiance of God's glory" (where Christ radiates from God or perhaps radiates for God) and "the reflection of God's glory" (where Christ has no light of his own and is ever reflecting God's glory).
The word is only used the one time in the NT but it is used in the Apocrypha one time:
22 for the artisan of all teaches me wisdom.
For in her is a spirit that is intelligent, holy,
unique, manifold, gentle,
movable, clear, undefiled,
distinctive, invulnerable, loving goodness, sharp,
unhindered, beneficent, 23 humane,
steady, secure, free from care,
all powerful, overseeing all,
and penetrating through all spirits
that are intelligent, pure, gentle.
24 For wisdom is more mobile than any motion;
and she pervades and penetrates everything because of her purity.
25 For she is the breath of the power of God
and the emanation of the pure glory of the Almighty;
because of this nothing defiled creeps into her.
26 For she is the brightness of the eternal light,
and the spotless mirror of the activity of God,
and the image of his goodness.
27 But although she is one, she is able to do all things;
and although she remains in herself, she renews all things;
and although she enters into holy souls ⌊in all generations⌋,
she makes them to be friends of God and to be prophets.
28 For God loves no one except the one who lives with wisdom.
29 For she is more beautiful than the sun
and above every constellation of the stars;
compared with the light, she is found to be foremost,
30 for night succeeds this,
but evil does not overcome wisdom.
8 But she reaches strongly from ⌊one side of creation to the other⌋,
and she manages all things well.
Brannan, R., Penner, K. M., Loken, I., Aubrey, M., & Hoogendyk, I. (Eds.). (2012). The Lexham English Septuagint (Wis 7:22–8:1). Bellingham, WA: Lexham Press.
It is also used by Clement:
1 Clement 36:
2 Through him we fix our gaze on the heights of heaven, through him we see the reflection of his faultless and lofty countenance, through him the eyes of our hearts were opened, through him our foolish and darkened understanding blossoms towards the light, through him the Master willed that we should taste the immortal knowledge; “who, being the brightness of his majesty is by so much greater than angels as he hath inherited a more excellent name.”
Clement I, P., Ignatius, S., Bishop of Antioch, Polycarp, S., Bishop of Smyrna, & Lake, K. (1912–1913). The Apostolic fathers. (K. Lake, Ed.) (Vol. 1, p. 71). Cambridge MA; London: Harvard University Press.
It is also used three times by Philo of Alexandria. I would argue that the rendering "ray" is unwarranted and should read "reflection":
Philo "On the Creation":
 Every man, in respect of his mind, is allied to the divine Reason, having come into being as a copy or fragment or ray of that blessed nature, but in the structure of his body he is allied to all the world, for he is compounded of the same things, earth, water, air, and fire, each of the elements having contributed the share that falls to each, to complete a material absolutely sufficient in itself for the Creator to take in order to fashion this visible image.
Philo. (1929–1962). Philo. (F. H. Colson, G. H. Whitaker, & J. W. Earp, Trans.) (Vol. 1, pp. 115–117). London; England; Cambridge, MA: William Heinemann Ltd; Harvard University Press.
 And mark how well the epithets that follow harmonize with that which was put first. The world, we read, is God’s house in the realm of sense-perception, prepared and ready for Him. It is a thing wrought, not, as some have fancied, uncreate. It is a “sanctuary,” an outshining of sanctity, so to speak, a copy of the original; since the objects that are beautiful to the eye of sense are images of those in which the understanding recognizes beauty. Lastly, it has been prepared by the “hands” of God, his world-creating powers
Philo. (1929–1962). Philo. (F. H. Colson, G. H. Whitaker, & J. W. Earp, Trans.) (Vol. 3, p. 239). London; England; Cambridge, MA: William Heinemann Ltd; Harvard University Press.
Here "in common" should read "by reflection":
Philo "The Special Laws":
 and therefore elsewhere he legislates on the subject of blood that no one should put either it or the fat to his mouth. Blood is prohibited for the reason which I have mentioned that it is the essence of the soul, not of the intelligent and reasonable soul, but of that which operates through the senses, the soul that gives the life which we and the irrational animals possess in common.
Philo. (1929–1962). Philo. (F. H. Colson, G. H. Whitaker, & J. W. Earp, Trans.) (Vol. 8, p. 85). London; England; Cambridge, MA: William Heinemann Ltd; Harvard University Press.
(123) ὅθεν ἐν ἑτέροις τίθησι νόμον περὶ αἵματος, μήθʼ αἷμα μήτε στέαρ προσφέρεσθαι· τὸ μὲν αἷμα διʼ ἣν εἶπον αἰτίαν ὅτι οὐσία ψυχῆς ἐστίν — οὐχὶ τῆς νοερᾶς καὶ λογικῆς ἀλλὰ τῆς αἰσθητικῆς, καθʼ ἣν ἡμῖν τε καὶ τοῖς ἀλόγοις κοινὸν τὸ ζῆν συμβέβηκεν. XXIV. ἐκείνης γὰρ οὐσία πνεῦμα θεῖον καὶ μάλιστα κατὰ Μωυσῆν, ὃς ἐν τῇ κοσμοποιίᾳ φησὶν ἀνθρώπῳ τῷ πρώτῳ καὶ ἀρχηγέτῃ τοῦ γένους ἡμῶν ἐμφυσῆσαι πνοὴν ζωῆς τὸν θεὸν εἰς τὸ τοῦ σώματος ἡγεμονικώτατον, τὸ πρόσωπον, ἔνθα αἱ δορυφόροι τοῦ νοῦ καθάπερ μεγάλου βασιλέως αἰσθήσεις παρίδρυνται· τὸ δʼ ἐμφυσώμενον δῆλον ὡς αἰθέριον ἦν πνεῦμα καὶ εἰ δή τι αἰθερίου πνεύματος κρεῖσσον, ἅτε τῆς μακαρίας καὶ τρισμακαρίας φύσεως ἀπαύγασμα — ,
Philo. (1929–1962). Philo: Greek Text. London; Cambridge, MA: William Heinemann Ltd; Harvard University Press.
So given the overwhelming evidence from our knowledge of the actual relationship that exists between the sun and the moon is that the moon reflects the sun (about 20% of the light) we should understand the new Jerusalem (the bride of Christ) to be lit by Christ's light, which reflects the light of the glory of God:
[Rev 21:23 KJV] (23) And the city had no need of the sun, neither of the moon, to shine in it: for the glory of God did lighten it, and the Lamb is the light thereof.
[Rev 22:5 KJV] (5) And there shall be no night there; and they need no candle, neither light of the sun; for the Lord God giveth them light: and they shall reign for ever and ever.
[2Co 4:6 KJV] (6) For God, who commanded the light to shine out of darkness, hath shined in our hearts, to give the light of the knowledge of the glory of God in the face of Jesus Christ.
This is the entry in the Exegetical Dictionary of the New Testament:
ἀπαύγασμα, ατος, τό apaugasma reflection
1. Ἀπαύγασμα occurs in the NT only in Heb 1:3. Verses 1:3f. are based upon a Christ-hymn that came into being in the Hellenistic Jewish Church and describes the way of Christ on the basis of the scheme: preexistence–death–exaltation (cf. Phil 2:6–11). The first line of the hymn (Heb 1:3a) describes the relationship of the eternal Son of God to God: ὅς ›ν ἀπαύγασμα τῆς δόξης καὶ χαρακτὴρ τῆς ὑποστάσεως αὐτοῦ. In agreement with Heb 1:3 Christ is called the ἀπαύγασμα τῆς μεγαλωσύνης (τοῦ θεοῦ) in 1 Clem. 36:2.
- The meaning of ἀπαύγασμα in Heb 1:3 is disputed. Actively, the word can denote radiance or effulgence (Philo Spec. Leg.. iv.123) or, passively, reflection or the light that is reflected (Wis 7:26; Philo Op. 146; Philo Plant. 50). The sentence structure in Heb 1:3 favors understanding ἀπαύγασμα and → χαρακτήρ as synonyms and, therefore, interpreting ἀπαύγασμα as pass.: Christ “reflects the glory of God and bears the very stamp of his nature.” Both predicates characterize the Son as the perfect image of God and thus correspond to the expression → εἰκὼν τοῦ θεοῦ (Col 1:15; 2 Cor 4:4).
In the background of the statement is the Hellenistic Jewish concept of the εἰκών. According to Wis 7:26 preexistent Wisdom is “the reflection (ἀπαύγασμα) of eternal light, a spotless mirror of the working of God, and an image (εἰκών) of his goodness.” In Philo the Logos appears as the “image” and “reflection” of God (Philo Op. 25; Philo Plant. 18; Philo Conf. 146f.; Philo Som. i.239 and frequently elsewhere). The εἰκών represents and reveals the invisible God and thus mediates the saving knowledge of God.
In Heb 1:3a—unlike 1 Clem 36:2—the accent is not on the idea of the mediation of revelation, but rather on the mystery of the person of the revealer himself. Both christological predicates underscore the divine origin, divine nature, and divine omnipotence of the preexistent One and in this they agree with the confession of Phil 2:6. The emphasis on Christ’s equality with God, further underscored by Heb 1:3b, has as its point of reference the statement in v. 3c regarding the atoning death: only the Son in the unity of his being and acting with God could bring about purification from sins through his death. Thus the work of redemption is inseparable from the person of the redeemer.