When I served at Ft. Ord in 1969, at Ft. Benjamin Harrison in 1969, and at Wharton Barracks, Heilbronn Germany in 1969-70, the weapon assigned to me was always locked in the armory, unless taken out for training reasons.
In other words, soldiers on and off duty did not carry firearms.
MPs presumably had firearms. Soldiers guarding the secure crypto-area had their rifle, and live ammo.
In the sixties I would pull guard duty both in the States and Germany. We were guarding tanks, APC's etc. and ammo. We were not issued ammunition.