I've owned a few 1965-1966 Mustangs over the years.
I don't see it being a rear wheel bearing, but you should replace them. You can pull them out without removing the brakes or draining the diff fluid. There is a tool, but I made one with a bolt and some washers.
Just grease them up and carefully tap the new bearing back in.
Did you try moving the rear wheels to the front (and vice versa) to be sure it isn't the wheel or tire? I've seen on several occasions when the tire balance machine was not calibrated properly.
Did you check the pinion on the diff? That bearing can fail and cause a vibration.
I'd check the main shaft on the auto transmission if all else fails. I've never had an auto, but the rear case can fail on a toploader. It will cause a big vibration.
Good luck.