I believe that Pilate's actions of washing his hands of Jesus' blood calling him ,a JUST person, as he put it, because in honesty he found no fault in him and the fact that he placed the Title above THE HEAD of Jesus confessing him King of the Jews shows that while he did not recognize the Truth in the flesh standing in his presence at first, by the time Jesus told him that he had no power over Jesus unless it be given him from on high, I do believe that Pilate began to BELIEVE.
Rather it was really God who had Pilate write that or Pilate on his own did it, by the fact that he went the steps to wash his hands with WATER shows that he did believe and wanted no part of it and I believe that he was saved due to it... faith without works is dead. But Pilate showed faith, it may have been a wavering faith, but even Peter denied Jesus 3 times in unbelief after Jesus died.. but we know he was saved.
Matt 27:22-26
22 Pilate saith unto them, What shall I do then with Jesus which is called Christ? They all say unto him, Let him be crucified.
23 And the governor said, Why, what evil hath he done? But they cried out the more, saying, Let him be crucified.
24 When Pilate saw that he could prevail nothing, but that rather a tumult was made, he took water, and washed his hands before the multitude, saying, I am innocent of the blood of this just person: see ye to it.
25 Then answered all the people, and said, His blood be on us, and on our children.
26 Then released he Barabbas unto them: and when he had scourged Jesus, he delivered him to be crucified.
KJV
John 19:19-22
19 And Pilate wrote a title, and put it on the cross. And the writing was, JESUS OF NAZARETH THE KING OF THE JEWS.
20 This title then read many of the Jews: for the place where Jesus was crucified was nigh to the city: and it was written in Hebrew, and Greek, and Latin.
21 Then said the chief priests of the Jews to Pilate, Write not, The King of the Jews; but that he said, I am King of the Jews.
22 Pilate answered, What I have written I have written.
KJV
He did not deny what he wrote and refused to retract it.... that says something!!