Once again, my memory is a little fuzzy and I really should know better than to post here without first re-testing, but here goes.
I had performed virtually identical experiments (even the use of plazas and statues!) some time ago (version 1.0, no patch). My results were almost exactly the same. I had even built a 100-tile loop and had the prefectures and engineers go all the way around -- in non-desert climates, they completed the circuit in time to prevent buildings from burning or collapsing.
A significant difference in results is that the walkers would usually go the full length indicated by Caesar Alan's "Long Patrol" distance (not one time in four). But occasionally they would start off heading toward their source building, pause, and turn around. On these occasions they would go the distance indicated by the "Short Patrol". I wonder if the road's orientation (NE-SW vs. NW-SE) makes a difference along with which end of the road the building is on (my tests were done on NE-SW roads with buildings on the NE end), or if it is just another difference in the versions.If I recall correctly, when I placed the source buildings in the middle of a length of road, the walkers always appeared on the same tile and always walked the "Long Patrol" distance from that tile. Caesar Alan, in your "mid-road" tests, did you measure the patrol from the walker's start tile or from the edge of the building?
As for school kids, they always appeared in the same place and always went by the same routes. Each went a different distance: 25 tiles, 20 tiles, 15 tiles, and 10 tiles (if memory fails me here, then they went 20, 15, 10, and 5 instead, or was it 25, 15, 10, and 5? ). Anyway, the location of the school determined the direction each kid went (sort of like whether or not four 1x1 houses form a 2x2). By carefully selecting the school's location, the two long-distance kids would run opposite directions and provide maximum coverage for a loop. For a 52-tile loop, coverage was usually only nearly complete with a few houses without coverage (I would replace those with non-housing).
quis enim ex vobis volens turrem aedificare non prius sedens conputat sumptus qui necessarii sunt si habet ad perficiendum