School students having been putting the signs out at pedestrian crossings for decades. Here’s how the scheme began.
School patrols began in New Zealand in the 1930s, and involved students waving flags from the roadside to warn drivers of children crossing. They didn’t have the power to stop traffic.
Dunedin’s Wakari School is said to have the first school patrol in the country. These early patrols were the brainchild of James Passmore, a founding member of the Automobile Association Otago.
His idea spread to schools around the country. A New Zealand Herald article from 1938 notes that apart from flag waving, “the patrols in the large schools mustered children and took them across the roads in batches, and thus prevented the dangers arising from jaywalking or straggling aimlessly about the streets.” 
The article notes that senior boys were selected by the headmaster for patrol duty. Other sources indicate that early road patrols in some schools were only seen as roles for boys.  This was changing by the mid-1940s.
The New Zealand Herald article quotes the head of the Auckland AA as saying “in all cases, it was intended that the work of school patrols should be directed and supervised by teachers, so that any idea that traffic control was in the hands of small boys might be discounted.”
By the early 1940s, it appears that confidence in the ability of young people to direct traffic on their local streets replaced any fears about such power. There was also a desire among public servants to create a standard road patrol system based on best practice in New Zealand and overseas. 
Giving students a means to stop vehicles in the street would require government intervention at the national level and this came with the passing of the Traffic (Road-crossing) Regulations 1944.
These regulations brought about the school patrol much as we know it today. It specified that local authorities could permit schools to run school patrols on official pedestrian crossings. The students would use a standard sign to indicate when traffic should give way.
“Every driver of a vehicle (including a horse-drawn vehicle and including the rider of a bicycle) when a patrol sign is extended at a crossing shall stop and thereby yield the right of way to school-children and other persons…” 
That same year, the Transport Department issued a booklet giving guidance to teachers and instructors on how to set up and run a school patrol.
From the booklet: "The underlying purpose of school patrols is to facilitate the safe, orderly, and expeditious crossing of the street by pupils on their way to and from school, and at the same time to create a minimum of delay to motor and other traffic passing along the street." 
The booklet has been updated many times since and is now known as the School Traffic Safety Teams Manual, published by the NZ Transport Agency.
 Reference Guide: Motoring Sources at the Hocken Collections.
 1938. 'Road Safety' in New Zealand Herald, volume LXXV, issue 23050, 30 May 1938. Retrieved from https://paperspast.natlib.govt.nz/newspapers/NZH19380530.2.122(external link)
 See for example “Juvenile Traffic Patrol” in New of the Day, Evening Post, volume CXXII, issue 39, 14 AUGUST 1936. Retrieved from https://paperspast.natlib.govt.nz/newspapers/EP19360814.2.60(external link)
 See “Girls now take their share…”, Evening Post, volume CXL, issue 93, 17 October 1945. Retrieved at: https://paperspast.natlib.govt.nz/newspapers/EP19451017.2.112.1(external link)
 H-40 TRANSPORT DEPARTMENT (ANNUAL REPORT OF).,Untitled, 1 January 1941. Retrieved from https://paperspast.natlib.govt.nz/parliamentary/AJHR1941-I.22.214.171.124(external link)
 The Traffic (Road-crossing) Regulations 1944. Retrieved from: http://www.nzlii.org/nz/legis/num_reg/tr1944316/(external link)
 H-40 TRANSPORT DEPARTMENT (ANNUAL REPORT ON),Untitled, 1 January 1945. Retrieved from: http://www.nzlii.org/nz/legis/num_reg/tr1944316/(external link)