I agree with Soldarnal but I think we can get even closer to the scripture John intends for us to "search and see." John is, in fact, working with many ironies in this passage. The Pharisees as teachers of the scriptures should know Isaiah 9:1-7.
The issue 7:40-43 and then extending through verse 52 is whether or not Jesus' coming from Galilee prevents him from being the Christ, the Son of David and or (the) Prophet. The people ask, "Is the Christ to come from Galilee?" and
"has not the scripture said that the Christ comes from the offspring
of David, and comes from Bethlehem, the village where David was."
The Pharisees also believe that "no prophet arises from Galilee" and challenge Nicodemus to prove them wrong by searching the scriptures. But what if we did, in fact, search the scripture as the Pharisees challenge? Galilee is only mentioned a few times in the Old Testament. The most prominent being Isaiah 9:1-7. And it's here that Isaiah prophesies,
But there will be no gloom for her who was in anguish. In the former
time he brought into contempt the land of Zebulun and the land of
Naphtali, but in the latter time, he has made glorious the way of the
sea, the land beyond the Jordan, Galilee of the nations. The people
who walked in darkness have seen a great light; those who dwelt in a
land of deep darkness on them has light shined... For to us, a child is
born, to us a son is given; and the government shall be upon his
shoulder, and his name shall be called Wonderful Counselor, Mighty
God, Everlasting Father, Prince of Peace. Of the increase of his
government and of peace there will be no end, on the throne of David
and over his kingdom to establish it and to uphold it with justice and
with righteousness from this time forth and forevermore.
It needs to be noted that the very next verse after John 7:52 is not 7:53 or any verse through 8:11. The earliest manuscripts do not contain this section. The very next verse is 8:12 and here Jesus says,
I am the light of the world. Whoever follows me will not walk in
darkness but will have the light of life.
Both the allusion and irony are biting. It is those who truly "know the law" who recognize Jesus (John 5:39) for who he is. For John, the Pharisees, who claim to know the scriptures, don't really know it at all.