I'd have to figure the running board tool box is just an owners common addition to the typical work truck of the 40's and 50's. I have to admit it's a natural place for a tool box. I've also seen gas cans,chain boxes and handyman jacks mounted there.(also a bucket of fence staples,once.) I'd put one on my '57 if it had running boards,but since it has a fleetside bed I'm stuck with a crossbed box and a couple of smaller fenderwell boxes.
I did score a BIG gangbox that now resides on my 62's flatbed. (still not enough room)
Speed


1954 GMC 350
1957 GMC 1/2 ton
1962 Chevy C-30
1952 Chevy 6400 dump bed project truck
'98 Harley FLSTC
'66 Pontiac Catalina
'76 Chevy 1 ton Duallie
'84 Bronco II
'78 Dodge W-200
'81 Toyota 4X4 truck