My son works in the motion picture industry. There are a few companies that rent out guns and equipment to the movie business. Only the very largest studios have much in the way of their own props anymore. But being qualified to tell people how to handle small arms is not quite a technical advisor.
Many films do have technical advisors, of course, but I suspect that the advice given is of an overall nature--and sometimes ignored. Gun handling is probably a small detail in a film, though I'd have to say it was often featured in the Westerns of the 1950s and some of the TV Westerns of that period. I believe actors sometimes received fast draw instruction, because that was sort of the thing at that time, but I wouldn't go so far as to claim it was historically accurate.
The movie "He walked by night," from 1948, was about the police trying to track down a killer in Los Angeles. There was a technical advisor on the set named Marty Wynn, who was or had been an LA police detective. One of the actors in the movie was Jack Webb, who in addition to being married to Julie London, went on to bigger things in television. Wynn supposedly suggested to Webb that a TV show based on real life stories from the police department (only changing the names to protect the innocent!) and that's where the idea for Dragnet came from.
I don't suppose too many war movies had technical advisors who were privates or riflemen during the war.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.