At the beginning of Chapter 12, Dimmesdale mounts the scaffold in secret. This is revealed within the very first few lines of the chapter. "Mr. Dimmesdale reached the spot where, now so long since, Hester Prynne had lived through her first house of public ignominy. The same platform or scaffold" where it all began (143). This is only one of the famous "scaffold scenes" from this novel, this one being a kind of culmination of Dimmesdale's self-hatred within the realization that he stands there safe and unseen while Hester has bore the brunt of their sin. Quite simply, Dimmesdale stands there on the scaffold to continue his self-condemnation for his participation in the sin behind Hester's famous scarlet letter. The fact that he stands there unseen, in the dead of night, highlights the minister's cowardice. "Without any effort of his will or power to restrain himself, he shrieked aloud; an outcry that went pealing through the night" (144). Dimmesdale's scream upon the scaffold highlights the minister's decaying mind due to extreme guilt.
Set in "an obscure night of early May", in chapter 12 we find Dimmesdale visiting the scaffold. This is the very scaffold on which Hester had first become infamous for her pregnancy.
He went up there in what could be argued to be an act of catharsis. He is picturing himself admitting to what he did and, for the first time, potentially accepting his guilt. Since Dimmesdale is a deeply flawed man who pretends to be a true leader of his flock, he only shows up at night. It was a coincidence that he sees Pearl and Hester, who were tending to the dying Governor Winthrop.
Something that stands out in this scene is that Hester continues to have some form of faith on Dimmesdale. Similarly, Dimmesdale continuously disappoints.
This happens when Pearl, who knows that she and her mother are to stand there again, asks Dimmesdale whether he will stand with them tomorrow the way that he is doing this night.
Not surprisingly, and despite of the clamors of guilt and redemption that Dimmesdale cries out in the heat of the moment, his answer is expected:
Wilt thou stand here with mother and me, to-morrow noontide?" inquired Pearl.
"Not so, my child. I shall, indeed, stand with thy mother and thee one other day, but not to-morrow!"
To put it colloquially, this is yet another proverbial "thanks, but no thanks" moment in the indolent relationship between Hester and Dimmesdale.