Take some pictures of the wheels and rear hubs. The one on the left front looks like an "artillery" wheel that were used on some 30s-40s GMCs. Some were 15" and some 16", maybe even bigger. All that I have seen are 6 lug. That would make your truck a 1/2 ton. 8 lugs would be 3/4 ton. I don't know if any of those wheels had 8 lugs. I also don't know how many lugs would be on a 1 ton of that vintage, possibly 5. But that would look like a big truck wheel. From the pictures the bed looks longer than a standard long bed.A guy here has a '37 or '38 1 ton pickup. I'll have to take a closer look at it.
Maybe I'll see that Stude on the salt.
