here are a few things about trailers in Florida.
trailers with an empty weight above 2000# get a title
trailers with an empty weight below 2000# get a registration only.
All trailers get a florida license and registration in florida.
to register a trailer in florida, you need an exact weight of the trailer supplied by the manufacturer for the VIN of the trailer (I have used emails from the trailer manufacturers), and you need the VIN, or you need to go to a scale and get the weight of your trailer only. You still need the VIN and paperwork.
you need to know your specific requirements per county. as far as countys go within Florida, some are harder than others to register a trailer and a boat.
how did you buy the trailer without knowing who the owner is? if you have prior registration or license for the trailer, you can find out who it was last registered to and go that route, or if you bought it at auction (like a storage lean type auction), then you need to follow that specific process outlined by the county tax assessor in the specific county.
Based on my experience registering trailers here that I legally owned in other states (and the headaches I went thru), it may be easier to buy a different trailer with valid paperwork.