"Overcome" vs "comprehend" in John 1:5
I believe that interpreting καταλαμβάνω as overtake or overcome in John 1:5 is preferred because such a meaning is more consistent with how John uses the term in the rest of the book, and because it better aligns with the good news theme expressed in John and the New Testament that we may have confidence in the light who overcame the dark domain because the darkness could not overcome him.
One strategy in determining authorial intent concerning the use of a word with more than one meaning is to review how the author might otherwise use the word elsewhere in the same work of writing you are reviewing where it may not seem as quite as ambiguous.
So let's do that and examine how John uses the word, καταλαμβάνω, throughout his Gospel writing:
3 The scribes and the Pharisees brought a woman who had been caught in adultery, and placing her in the midst 4 they said to him, “Teacher, this woman has been caught in the act of adultery.
In our first example (which is actually two, but we'll count as one), John uses the term to describe the woman being apprehended or arrested for her crime of adultery. (It's noteworthy that the word "apprehended" seems to carry with it a very similar range of meaning that καταλαμβάνω does)
35 So Jesus said to them, “The light is among you for a little while longer. Walk while you have the light, lest darkness overtake you. The one who walks in the darkness does not know where he is going. 36 While you have the light, believe in the light, that you may become sons of light.”
Our second and last example is quite interesting since we see καταλαμβάνω used in the context of light and darkness similar to the way it is used in John 1:5.
Here it is quite apparent that Jesus is not concerned about the darkness comprehending his disciples but taking and using them for its own purposes. In this verse walking in the light prevents the darkness from overtaking the disciples, presumably, because the light cannot be overtaken by darkness as John 1:5 expresses if we assume the same meaning for καταλαμβάνω in 1:5 as we have for 12:35-36.
The parallel usage of καταλαμβάνω in 12:35-36 in comparison to 1:5 seems pretty decisive on its own as to how it should be understood.
Now for me, I quite like @Jas3.1 argument that interpreting καταλαμβάνω as comprehend seems to flow quite well with the themes of John 1 of revelation, perception, testimony, logos, and belief.
However using καταλαμβάνω to strengthen the imagery of the Jesus as the true light that could not be overcome by the darkness better aligns with a significant theme of the good news of Jesus Christ as he declares elsewhere in the book, "...the ruler of this world is coming. He has no claim on me (John 14:30)," and ..."take heart; I have overcome the world (John 16:33)."
You see, by Jesus not being overcome by the kingdom of darkness, Jesus overcomes the kingdom of darkness.
8 And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross. 9 Therefore God has highly exalted him and bestowed on him the name that is above every name,
For what the law was powerless to do in that it was weakened by the flesh, God did by sending His own Son in the likeness of sinful man, as an offering for sin. He thus condemned sin in the flesh,
He disarmed the rulers and authorities and put them to open shame, by triumphing over them in him.
1 Corinthians 15:56-57
56 The sting of death is sin, and the power of sin is the law. 57 But thanks be to God, who gives us the victory through our Lord Jesus Christ.
John also riffs off Jesus' conquering theme in his other writings:
1 John 4:4
4 Little children, you are from God and have overcome them, for he who is in you is greater than he who is in the world
10 And I heard a loud voice in heaven, saying, “Now the salvation and the power and the kingdom of our God and the authority of his Christ have come, for the accuser of our brothers has been thrown down, who accuses them day and night before our God. 11 And they have conquered him by the blood of the Lamb and by the word of their testimony, for they loved not their lives even unto death.
Circling back to John 1:5, here we have expressed not simply that the true light is not comprehended by darkness, but that our hope in the light is secure because it cannot be overcome by forces of darkness that has ensnared and enslaved us for so long.
Hebrews 2:14-15 14 Since therefore the children share in flesh and blood, he himself likewise partook of the same things, that through death he might destroy the one who has the power of death, that is, the devil, 15 and deliver all those who through fear of death were subject to lifelong slavery.
I believe that interpreting καταλαμβάνω as overtaking or overcoming in John 1:5 is preferred because such a meaning is more consistent with how John uses the term in the rest of the book, and because it better aligns with the good news theme expressed in John and the New Testament that we may have confidence in the light who overcame the kingdom of darkness because the darkness could not overcome him.