In the early years of the Vietnam war the 25th Infantry Div in Hawaii would provide a platoon of Infantry gunners at a time to some units. this continued until well into 1965 as far as I can determine. Maybe even longer. Someone who has done better reasearch than I, may answer in more detail.
The UH 1 was designed for the aircraft commander or a single pilot to fly from the right hand seat. That is the side with the most complete set of controls and instruments and also frees the left hand of the pilot to operate the radios and stuff.
Due to the way the instrument panel is off set to the right( to accomodate the greater number of instruments) there is a much greater external view from the left had seat. Since most of 1, 2 and 3 corps have jungle, there were a lot of very tight landing zones with very tall trees.
The more experienced pilots (the Aircraft Commanders) chose to sit on the side with the best external vision so they could operate in the tight landing zones. As the war progressed it became a sign of prestige to fly slicks from the left side because that is where the AC and Instructor pilots sat and it took hold.