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.)
It looks like the (US) industry term is flagger, that is, if it's not specifically a traffic cop.
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.
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".