Pickups did not come factory equipped with 312’s in the U.S. but 3.89:1 gears were popular in many of the early Sixties pickups such as yours when equipped with a standard 3 speed tranny. You didn't mention what transmission you're dealing with and that's part of the equation.
Automatic transmissions typically had gear sets that were smaller numerically than standard transmission equipped cars. As the cars got newer, they came equipped with numerically smaller gearing (less steep) which fell in line with the improvements in the torque band that was occuring. A ’57 car with a 292 and automatic came with 3.10’s while the standard transmission version w/o overdrive would be a 3.56:1. With overdrive, the rear gear would be 3.89:1. My ’50 with V8 and overdrive came with 4.27:1 rear axle while my ’54 Ford with overdrive came with 4.10:1 rear gears. My '55 with 272 and O.D. came with 3.89:1 rear gearing. I’ve since changed the rear gears in my ’55 Customline to a set of 3.56:1’s which compliements the upgrades I've performed to the 272. On the flip side, my '69 Torino with 428 and 4 speed originally came with 3.25:1 rear gearing. This is all just food for thought.