What is Dimmesdale's most characteristic gesture, and how does it link him with Hester?

Dimmesdale's most characteristic gesture is when he places his hand over his heart. Though we don't find out for awhile.... Dimmesdale has marked his own breast to match Hester's.... thus he carries her shame, though it is unseen.

"They mostly do," said the clergyman, griping hard at his breast, as if afflicted with an importunate throb of pain.

And thus, while standing on the scaffold, in this vain show of expiation, Mr. Dimmesdale was overcome with a great horror of mind, as if the universe were gazing at a scarlet token on his naked breast, right over his heart. On that spot, in very truth, there was, and there had long been, the gnawing and poisonous tooth of bodily pain.

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Now, at the death-hour, he stands up before you! He bids you look again at Hester's scarlet letter! He tells you, that, with all its mysterious horror, it is but the shadow of what he bears on his own breast, and that even this, his own red stigma, is no more than the type of what has seared his inmost heart! Stand any here that question God's judgment on a sinner! Behold! Behold, a dreadful witness of it!"

With a convulsive motion, he tore away the ministerial band from before his breast. It was revealed!