After releasing the internal latch, you'll then need to go to the front of the car and lift the hood. There's usually a small lip or handle at the very front of the hood, near the grille, that you can use to help lift it.
Because the location can vary slightly depending on the specific model and any modifications made to the vehicle, a picture of the dash or a consultation of a 1960 Thunderbird owner's manual would be beneficial for pinpoint accuracy.