The Dubious History of Pun (Pun Among Other Pungent Words)

A question about the origin of pun. Our correspondent noticed that pun and pundit appeared in English at nearly the same time, that a pun “heaps together” different meanings (so Skeat), while the root of pundit (Sanskrit for “learned man”) also means “to heap, pile up.” Moreover, bunk “berth” may likewise go back to a word for “heap.” Is it possible that pundit and bunk provide a clue to the origin of pun?
The Dubious History of Pun (Pun Among Other Pungent Words)