I did a quick Google search of the US Constitution's 20th amendment, and it seems to me like section 1 doesn't specify a timezone.
The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.
What timezone does the section follow?
This answer had me curious.