I have a 4-6-2, but no 2-8-2.
Assuming it is the same screw they used in the 4-6-2:
It is a flat-head, M1.4, shoulder screw
Total Length: 11.6 mm
Shoulder length: 5.25 mm
Shoulder diameter: 2 mm
Head diameter: 3 mm
I have a lot of shoulder screws, but nothing like this. If I were you, I'd just get an M1.4 screw about 1/2" long, and slip a sort bit
of brass tube over it to create the larger smooth shoulder part by the head.