Ἦν τὸ φῶς τὸ ἀληθινὸν ὃ φωτίζει πάντα ἄνθρωπον ἐρχόμενον εἰς τὸν κόσμον.
ἐρχόμενον is accusative masculine singular, meaning it refers to "each" (πάντα—accusative masculine singular) "man" (ἄνθρωπον—accusative masculine singular) as in "every man."
Its sense is, therefore: "[all men] that come" ("into the world...," and so on).
It cannot refer to the neuter "light" (φῶς). This would be equivalent of writing, "His name is Paul, and it authored most of the epistles in the New Testament." Either you are abruptly introducting a new object/subject, redefining the gender of the subject; or, as I can only suspect is the case with some translations, referring back to a subject of which the beginning of this sentence is a description (namely, the Word is a "he," but is also "the Light," which is neuter). (If nothing else, 1:8 shows us "the light" can be mistaken for a masculine person—ἐκεῖνος and so it isn't unreasonable to translate it the 'other' (NASB) way, taking the above into consideration).
However, the straightforward reading is "That was the true Light which enlightens every man that comes into the world." At least, isolated, it needs to be translated this way (i.e. unless the one for whom "the light" is a title or description is nearby identified, and as masculine).
In other words "the light, having come into the world,..." is a contextual, rather than theological, interpretation.
The relation of life, light and the Logos it concerns, is a wholly theological one, but that doesn't mean St. John doesn't elsewhere speak of it, and therefore 'agnostic' hermeneutics apply.
Namely, in John 8:12, he relates something Jesus said about Himself:
Πάλιν οὖν αὐτοῖς ἐλάλησεν ὁ Ἰησοῦς λέγων Ἐγώ εἰμι τὸ φῶς τοῦ κόσμου ὁ ἀκολουθῶν ἐμοὶ οὐ μὴ περιπατήσῃ ἐν τῇ σκοτίᾳ ἀλλ’ ξει τὸ φῶς τῆς ζωῆς
Again therefore, Jesus spoke to them, saying, I am the light of the world: they that follow me shall not walk in darkness, but will have the light of life.
This seems to indicate that the "light" spoken of by John, which he evidently gets from Jesus; that is, the "enlightening" of every man (Jn 1:9); means vivification, quickening. That is, "light of life" means either that the light is the life, or that the light is the full enjoyment of life—true life.
Jesus, of course, is giving moral weight to the terms 'dark' and 'light.' And many throughout the centuries have seen in Genesis 1:4, taken with John 1:5 from being the divide between good and evil in general, but more specifically (or at least one specific example) the evil (or reprobate) angels and the good angels, and those who are of, or support, the respective of sides (cf. Wis 2:24; Mt 6:21-24).
This seems to be related to the quote-unquote theology of personified Wisdom (cf. Lk 7:35; 11:49), where She is said to permeate and comprise all things (very much in line with Greek thought on the common Logos which 'binds' all things—the presupposition that underlies all, if you will; reason, logic: "without Him was made nothing that has been made," although John clearly has a spoken "Word" in mind if not exclusively, then primarily). See Wisdom 7:24-27; cf. Hebrews 1:3.