Argosy Camper Trailer

VIN Standardization came in 1981, as others mentioned. But there were VINs prior to 1981, and when a manufacturer didn't use a VIN, they used a serial number. Each manufacturer had their own process for establishing some sort of VIN and/or serial number conformity, within their product line, as noted in the Airstream example above.

As someone involved in Public Safety/Law Enforcement prior to retiring, I ran a LOT of VINS/SN in my career. Finding them was sometimes difficult, and finding something in the various state databases was even more of a challenge. Also, in the early days, NADA and NHTSB published VIN configuration books (pre-internet), that showed the VIN location and the VIN structure for most manufacturers. You might want to check your local library to see if perhaps they have some of those old books, probably in archive. Because of the plethora of formats, the VIN Standardization Act came into being.

VIN = NIY. Not invented yet. The number you've found is a manufacturer's serial number.

A trailer sitting in a park for a long time may not have been titled as a vehicle, they could have been carrying it as commercial or personal property, or even real estate. RVs can cross over to different tax domains.

I don't know the rules in Florida. It might be titled as a trailer, or as an antique vehicle. You might need to hire a lawyer to run it through the process. I know Oklahoma, it doesn't need a title here.

a few years back , I bought an old travel trailer, bill of sale.. no title (here in Calif)
pulled it to the DMV, they did an inspection, found the serial, did a computer check... not stolen, issued a new title

i ended up gutting the trailer and using it for parts storage, old Honda mopeds and parts

1972 doesn't have a vin number- only the serial number. There should be a letter before the first 20.See here for decoding info.
It will likely be a bit of a pain to do a quiet title, but could be worth it.

The titling question sounds like something you should ask of the state department of transportation; the rules and regulations and procedures vary widely. In my state of Vermont, it would be quite simple—they won't issue a title for a vehicle over IIRC 16 years old, nor require one when registering it.

VINs were standardized in 1981, so you'd probably just have some sort of a manufacturer's serial number. Presumably that's what you found.

They may not have been titled back that far. I know that NY and Florida are apples and oranges, but any vehicle in NY older than 1973 does not require a title.
NHTSA standardized VIN format in 1981. Try the number you have,probably a serial #