I saw the Elvis Presley movie last evening, and noticed the tanks and trucks shown look like a glossy dark green. Standard color for that time and place, or specifically for the unit featured in the movie?

That's the classic dark olive drab of the fifties and sixties. Color photos of trucks in Vietnam show vehicles that are nearly black. And vehicles were sprayed with fuel to get them even glossier for parades.

Some builders use Model Master US Army Helicopter drab to capture it. (4723. supposedly FS 34031) It's a dark greenish-grey OD.

That glossy green was standard in the 50s and early 60s. This reminds me of an incident I experienced in the 2nd Division in Korea in 1987. We had a Signal Bn commander who was very "spit and polish" when it came to the barracks and the BN vehicles-- too much so in fact. He regularly gave BN punishment for minor inspection infractions, which had a very devisive effect on moral. He also tired of the dull matt finish on his CARC painted vehicles, he ordered every one of them to be waxed with a carnuba wax finish. When that didn't work well, he used olive oil and a spin buffer to polish each CARC painted vehicle into a beuatiful green shine. He was relived of command shortly thereafter because the CARC properties were totally destroyed (moral too). It cost the Division about $500K to repaint the entire BN. But they sure were shiny! It's frowned on for commanders to reduce their unit effectiveness for cosmetic reasons.
VR, Russ