Answer:
Based on a conversation with a CFPB attorney last year, when one of the fixed-date federal holidays falls on a Sunday but is observed by the federal government on Monday, the Monday date is a business day (precise Reg Z definition) whether the bank is open or not, for the counting of business days involving the right of rescission, certain TRID timing rules, and a provision dealing with private education loan disclosures.
As for the idea that there is a connection between the precise business day definition and U.S. Postal Service's business days, there is no truth to it. The post office's schedule is irrelevant.