"Baaaaak in the day............" cars towed a lot of trailers. On our farm we often put 3 wagons with 12+ TONS of grain behind our 64 Galaxie with a bumper hitch just like pictured below.
Was it safe?? Never had a problem, so it must have been, right? Did we go far??? no Did we go fast??no Were there any cars in the traffic that could stop better than us??no We got away with it without any brakes other than the drums on the car!!
In short, local use you might get away with it, but for any distance or speed in today's mix of vehicles that have vastly improved brakes, I would think long and hard about doing it. Even if you are alert in a modern car, the chances are you will rear end the vehicle ahead of you should it be equipped with computer controlled braking in an emergency situation. Enjoy your Thunderbird however you choose. They were meant to drive and will certainly step up to the task, but be safe.