I think you are correct per NEC. Historically I seldom see a ground rod at a construction trailer although I am at a loss as to what Code Article would exempt it.
Need article number
Need article number
Structure. That which is built or constructed.
I don't see how a construction trailer can be classified as a "home" of any kind.
One could argue it is a structure, as it seems to fit the definition of a structure. However, I am not sure it is really a structure as one could argue it is manufactured and not constructed.
I also agree it is temporary and thus might well be wired per 590, which would seem to require you to provide a GES IAW article 250.
What's a "construction trailer?"
If you mean one of those job-site offices, then 550 contains language that make clear that the article applies, that such trailers are within the scope.
If you mean something with wheels, that's filled with your tools and transported around all day, then the NEC has limited application. Your rolling workshop is essentially a big appliance, and no ground rod is needed.
550.1 Scope. The provisions of this article cover the electrical
conductors and equipment installed within or on mobile
and manufactured homes, the conductors that connect
mobile and manufactured homes to a supply of electricity, and
the installation of electrical wiring, luminaires, equipment, and
appurtenances related to electrical installations within a mobile
home park up to the mobile home service-entrance conductors
or, if none, the mobile home service equipment.
(A) Mobile Home Not Intended as a Dwelling Unit. A
mobile home not intended as a dwelling unit ? for example,
those equipped for sleeping purposes only, contractor?s
on-site offices, construction job dormitories, mobile
studio dressing rooms, banks, clinics, mobile stores, or intended
for the display or demonstration of merchandise or
machinery ? shall not be required to meet the provisions
of this article pertaining to the number or capacity of circuits
required. It shall, however, meet all other applicable
requirements of this article if provided with an electrical
installation intended to be energized from a 120-volt or
120/240-volt ac power supply system. Where different voltage
is required by either design or available power supply
system, adjustment shall be made in accordance with other
articles and sections for the voltage used.