For those who hold that John 1:1 is about a Genesis beginning, how do they explain the light coming after life?

A brief answer, to a brief question, perhaps better suited for Hermeneutics.SE:

• Christ's life embodied the light of his own teachings.

• Seeing the way he lived his own life, became a light unto those witnessing its sanctifying power.

Many other rabbis also preached, but, as Christ's own brother so beautifully puts it:

^{James 1:22} But be ye doers of the word, and not hearers only, deceiving your own selves.

Similar concepts are also echoed in the following pasages:

^{Matthew 5:14} Ye are the light of the world. A city that is set on an hill cannot be hid. ¹⁵ Neither do men light a candle, and put it under a bushel, but on a candlestick; and it gives light unto all that are in the house. ¹⁶ Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven.

^{Luke 8:16} No man, when he hath lighted a candle, covers it with a vessel, or puts it under a bed; but sets it on a candlestick, that they which enter in may see the light. ¹⁷ For nothing is secret, that shall not be made manifest; neither any thing hid, that shall not be known and come abroad.

^{Luke 11:33} No man, when he hath lighted a candle, puts it in a secret place, neither under a bushel, but on a candlestick, that they which come in may see the light. ³⁴ The light of the body is the eye: therefore when thy eye is single, thy whole body also is full of light; but when thy eye is evil, thy body also is full of darkness. ³⁵ Take heed therefore that the light which is in thee be not darkness. ³⁶ If thy whole body therefore be full of light, having no part dark, the whole shall be full of light, as when the bright shining of a candle doth give thee light.

I think you're inventing a contradiction that doesn't exist.

In Genesis 1, light is first (1:3), then there is life (1:11).

This, first off, is not strictly true. There is life in God (and/or in Christ; a Trinitarian would of course say that God and Christ are the same, so both are true), but this is an eternal attribute of God/Christ. There is not a beginning of "life". The creation of plants represents a manifestation of life, yes, but to say that there was not life is on par with saying there is no love, or goodness, or anything else that is a defining attribute of God. This in effect means the God Himself cannot exist without Creation, which is of course nonsense.

In John 1, life seems to come first (1:4a), but that life then is the light of men (1:4b).

John 1:4 is certainly talking about a metaphorical "light". In particular, v5 is metaphorical; the "darkness" is sin, which did not exist before Creation, while the light is eternal. (Note however there is a difference between God 'being' light and allowing that to manifest in Creation.) Note also the parallel with Revelation 21:23; I (and I think many) would argue that the "light" is the same in both locations.

Revelation may or may not also indicate a literal, physical light. Similarly, the "light" of Genesis 1:3 may or may not be, in some literal sense, God's glory being allowed to enter Creation. While an argument for that has been made, and it certainly strengthens the claim that the "light" of Genesis 1:3 and John 1:4 is the same, I don't claim that this is necessary to an understanding of John 1:1-3 as referring to the Genesis 1 Creation.

In any case, we've already established that the "life" is an eternal attribute of God/Christ which preexists Creation. Moreover, "the life was the light of men" does not establish the supposed chronological relation.

Consider a light in a room. Consider also a potter who turns on the light and makes a pot. One can say that the light is "the light shining on the pot", but this does not mean that the light didn't exist before the pot. Similarly, even if we accept the claim that "life" as used in John 1 didn't exist until the third day of Creation, the "light of men" can't exist as a concept until men exist (on day six). But this does not mean "light" didn't exist before then, merely that it didn't take on the specific of being "the light of men" until later.