Summary: Someone shows that they are a follower of the "Father of Lights" through their: 1) Words (James 1:19-21), 2) Walk (James 1:22-25), 3) Works (James 1:26-27).
A common thing in extended family gatherings is to compare how siblings look. Some tend to look like their mother, others like their father, some have mannerisms and temperaments that are similar, while others have similar interests or occupations.
In Gen 1:26–27 we see that humans are made: imago Dei, in the image or God, reflecting the divine likeness. In which ways are we reflecting the image of God? Can we tarnish this image and how does God, who can be described as the "Father of Lights" have His image reflect in us because of His light.
To answer these questions we must first ask who is this Father of Lights:
As James 1:17 says "every good gift and every perfect gift is from above: which means that the perfect, flawless, holy goodness of God results in His doing and giving only what reflects His perfect holiness and truth. His works reflect His character. Negatively, James is saying that, from temptation to execution, God has absolutely no responsibility for sin. Positively, he is saying that God has complete responsibility for every good gift, and that every perfect gift that exists has come down from above.
The Father of lights was an ancient Jewish title for God, referring to Him as Creator, as the great Giver of light, in the form of the sun, moon, and stars (cf. Gen. 1:14–19). Unlike those sources of light, which, magnificent as they are, can nevertheless vary and will eventually fade, God’s character, power, wisdom, and love have no variation or shifting shadow.
God’s benevolence is like a light which cannot be extinguished, eclipsed, or “shadowed out” in any way at all. The light of the sun may be blocked, for example, by some material object, so as to cast a shadow: indeed, for a time in an eclipse, the direct light of the sun (or moon) may be shut off from the observer. Nothing like that can block God’s light, interrupt the flow of his goodness, or put us “in shadow,” so that we are out of the reach of his “radiance.” It is not necessary to confine “shadow” to eclipses or any other specific sort of shadow. God’s light or radiance lets nothing stop it (Adamson, J. B. (1976). The Epistle of James. The New International Commentary on the New Testament (75). Grand Rapids, MI: Wm. B. Eerdmans Publishing Co.).
Hymn: Horatius Bonar expresses a similar thought in his fine hymn:
Light of the world! for ever, ever shining,
There is no change in Thee;
True Light of Life, all joy and health enshrining,
Thou canst not fade nor flee.
In James 1:18 the phrase "of his own will" translates the aorist passive participle of the verb boulomai, which expresses the idea of the deliberate and specific exercise of volition. The phrase is also in the emphatic position in the Greek, reinforcing the truth that God’s sovereign and uninfluenced will is the source and basis of the new life.
That "he brought us forth" is from the same verb rendered “gives birth” in verse 15. God always takes the initiative (AORIST PASSIVE [deponent] PARTICIPLE) in mankind’s situation and salvation (cf. John 6:44, 65; Rom. 9; Eph. 1:4; 2:8; I Pet. 1:3) (Utley, R. J. D. (2000). Vol. Volume 11: Jesus’ Half-Brothers Speak: James and Jude. Study Guide Commentary Series (21). Marshall, Texas: Bible Lessons International.).