According to grammar rules, a comma is necessary for sentence 2. The "pause" rule is used just to help grammar students when trying to determine when to put a comma. A comma is not needed for sentence 1 because "he works for a bank" is an adjective clause, with "because" as the conjunction; it's modifying or describing why John is rich. In sentence 2, the second independent clause is not describing the first clause, and therefore needs a comma. If the first sentence said, "John is rich, and he works in a bank", you would need the comma, because then the second clause is not describing the first clause.