The first thing to do, is see if you can find a copy of a "Table of Organization and Equipment" (TO&E) for a US Armor Division in WW II. I wish my dad was still around, because he had all that stuff and would probably have known the answer off the top of his head. In any event, the TOE will tell you what vehicles (if any) were allocated to maintenence sections in the letter companies and the HQ and Service companies of the various battalions within the Division. Once you determine for example that the Service Company Battalion maint platoon had several trucks of a certain size (2 1/2 ton), you could go from there. The TO&E might even indicate that a certain model, as has been suggested, specifically designed for maint was allocated.
A word of caution. The presence of something on the TO&E in NO WAY guarantees the unit actually had the equipment. And without a specific photo for example, you'd probably never know for sure whether the truck had a metal factory supplied, or a wooden unit fabricated "hootch" on the back, nor if the bumper number was SVC 12 or SVC 21.
But the good news is, that anyone ELSE looking at your build won't know either!!!!! :-)
I'll try to dig through some stuff and see if I can find out what was allocated. I went through this a while back trying to figure out whether tank companies in the tank battalions did or did not have M32 recovery vehicles. (The answer I got was yes, there was 1 per letter company and 3 in the maint plt in Service Company)
But for what it's worth, I'll just about guarantee, that SOME unit SOMEWHERE built a hootch out of wood on the back of a 2 1/2 ton and put in shelves and work benches and the truck had a winch on the front!!!
Tom