In VT trailers that old wouldn't get a title. All you will need is a bill of sale.
From NYSDMV's website:
Trailers - model year 1973 or newer with an unladen weight of 1,000 lbs. or more
The acceptable proof of ownership is a NYS title certificate or the acceptable proof of ownership from another state, and a bill of sale. The person whose name appears on the proof of ownership must sign the transfer section of the proof of ownership.
If the trailer is registered in another state, contact that state to make sure that the proof of ownership you receive is the acceptable proof of ownership for that state.
Trailers - model year 1972 or older, or any trailer with an unladen weight of 999 lbs. or less
The acceptable proof of ownership is a transferable NYS registration or the acceptable proof of ownership from another state, and a bill of sale. The word "transferable" must appear on the front of the registration. The person whose name appears on the registration must sign the transfer section of the registration.
If the trailer is registered in another state, contact that state to make sure that the proof of ownership you receive is the acceptable proof of ownership for that state.
Am I missing something or does that not have a ball hitch?
The photos show and the ad states that the trailer has a pintle hitch.
Also - you may be able to register it as home made, but that requires getting the trailer weighed and some other things. I'm sure that DMV's website could tell you the requirements. I did this once several years ago but can't remember everything that needed to be done.