The AM32 trailer uses M37 rims I believe, 5-bolt lugs. That trailer the OP posted looks to be 6-bolt lugs, bigger trailer.
It looks like a lot of things that came out of the bombing ranges out west, that were used during the Cold War. There are countless modifications and variants of all sorts of weird equipment coming out of those bases, used from the late 40s to the 80s, when we tested all sorts of gear and the specialized equipment that went along with it. I searched Google with multiple combinations of terms, nothing like this trailer came up. I'm afraid, unless you or the seller can provide a data plate or some other official way to ID this, it may just be chalked up to one of those custom pieces of equipment the Air Force bought.
If you bought it, how did you plan on titling it in your name? As a homemade trailer?