Thank you for your question. I look forward to working with you to provide you the information you are seeking for educational purposes only.
You will need a copy of a bill of sale, which should be notarized and fill out a form for application for title without title/registration form: https://www.flhsmv.gov/dmv/forms/btr/82040.pdf with your local DMV or tax assessor's office. You will need to get the VIN checked by local law enforcement as well and most times they will tell you the last place the vehicle was registered. Most times FL will accept the notarized bill of sale and VIN check that the vehicle is not stolen and has no liens (it shouldn't from 1924). You also need proof of insurance.
If they refuse, then your only other way to register it would be to file a suit called "Petition to Quiet Title" and you have to serve the last known registered owner and seller and the court would have to clear the title for your ownership.