I’m going to use the example of the TV series Stargate SG1 for this question. Throughout the series, Daniel Jackson (historian/archaeologist/geek) will refer to something that happened in an ancient earth civilization or how writings discovered mirror certain ancient earth languages. Sometimes I will get on the internet and try to verify this random mentioned fact and sometimes it’s true and of course for the sake of a show completely fictional. So my question is are there historians or archaeologists that come in and assist with getting some of this information correct? Something like “historical reference director” or anything like that?
I do know a little bit specifically around Stargate SG-1, and the answer there seems to be no, they didn't use historians or archaeologists as consultants, at least from what Michael Shanks has stated in interviews.
In effect, the writers took very broad interpretations of ancient Egyptian mythology (and other ancient cultures on occasion) but changed what they needed in order to make plots work. Usually this is fine, although personally the worst offender episode where they do this is "Demons", where they go to a planet that is supposed to stuck in the European Middle Ages, and then they (and our knowledgeable Dr. Daniel Jackson) repeat practically every popular myth about Medieval society.
To your broader question: historians working as consultants for movies, television programs, documentaries, and even video games is definitely a thing, and the American Historical Association talks about that work on their site here
Relevant passage:
Producers of documentaries, dramatic films, and educational programming often hire historical consultants to advise on costumes, scenery, props, dialect, and content accuracy. Most television networks and large production companies will require the services of a historian, and some consulting firms specialize in media productions and the entertainment industry.
I think the key word to take out of that is "advise". In general, a production will have something in mind, hire a historian as a consultant, and ask them how accurate something is - usually it's on the level, as the blurb notes, of things like scenery, dialect or costuming. I focus on the "advise" part because the production is always free to disregard what the historical consultant's opinion.
"Historic accuracy" and the use of historic consultants can be a double-edged sword. For example, director Ridley Scott touted the historic accuracy of his 2010 Robin Hood, and while by my understanding the depictions of details of village life in late 12th century England were accurate, and while the story uses real historic figures (mostly), overall the story is fictional and not terribly true to history (the English didn't defeat a French invasion at the Cliffs of Dover in 1199).
Sometimes having a "historic consultant" can lend cover to questionable accuracy. I'm particularly thinking of how Anne Applebaum acted as a historic consultant to director Peter Weir in the production of The Way Back.
Applebaum wrote a history of the Soviet gulags, but isn't an academic historian, which I'm not saying one needs to be, but still it's worth noting. And as I understand it, her input around historic accuracy in the depiction of Soviet Gulags was well-received, and accurate. But it's in the service of a film marketed as "inspired by real events", yet based on a memoir by Slavomir Rawicz that is more or less considered a hoax (and even Weir stated it's "essentially a fictional film").