Carl -- Probably something early '30's or older. After that, the grills get too curved (like the '38 - '40 grills or even the '41 to '47 1st grills) and the dogs would just roll off into the coals. You could invert them, I suppose, but then the dogs would just roll down to the bottom and wouldn't cook thoroughly. The Advance Design and newer trucks have grills that are too open -- wouldn't hold anything very well other than, say, a rack of ribs or a whole bologna.
If someone shows up at Winchester with an early '30's truck, lets remove the grill and try it to see if my hypothesis is correct. I'm sure the owner wouldn't mind. You remove the grill, I get the dogs from Billy.
Well, for this plan to work we will need another accomplice to create a distraction like brush fire. We will also need to bring in someone else to remove the grill since I won't be able to make it. I am going to Southern Illinois to the in-laws to catch a groundhog living under the barn and to get a Model T started.