I'm referring to people in bright orange or green vests who direct automobiles. I thought of road workers, but it's not specifically around road work. Is there a word for "traffic-directors"?
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If they're police officers, than as Gnawme says the common term is "traffic cop".
Construction workers who are working on a road or something near a road so that they are interfering with traffic will normally have one of their members direct traffic. This person used to be called a "flagman". In these politically-correct days, he or she is now called a "flagger". (While I don't have statistics on this, from my anecdotal observation, these days if the construction crew is more than 2 or 3 people the flagger is almost always a woman.)
In the UK such people who are not police are called traffic marshals, or, when directing traffic (say, fork-lifts or lorries being unloaded) within a yard, banksmen.
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If the person directing traffic is a policeman (or woman) then traffic cop is perfectly acceptable. Traffic wardens are non-police ("civil staff") members of police forces with special responsibility for managing traffic, including parking.
It looks like the (US) industry term is flagger, that is, if it's not specifically a traffic cop.
In Canada, depending on the sex, it is traffic police(wo)man, or as someone rightly pointed out, 'cop', but that is very informal.
I have seen in construction literature (I have done a bit of everything, haha) that they still call the road workers "flag men" despite there being more women in the business now. When I was corrected verbally, I was told "flag person".