Specifications in the original literature for vintage Mustangs (shop manuals/owners manuals) specify 24 pounds per square inch (psi) for tire pressure. But tire technology has changed considerably during the past 30-35 years.
When Mustangs were new, they came with bias-ply tires. Most modern tires are radials, with maximum pressures of as much as 40 or 45 psi cast into the tire by the tire manufacturers. (That's maximum, not necessarily recommended.)
Correct tire pressure is dependent on several variables, including car weight, weather/road conditions, and personal expectations. Lower pressures, and therefore softer tires, will result in better handling and traction; higher pressures will result in better gas mileage. But higher pressures also result in a rougher ride; too high will cause uneven wear down the center of the tire.
The Mustang-specified 24 psi is probably too low, while the maximum pressures of 40+ psi is probably too high.
When this question was asked on the Vintage Mustang Forum, replies were in the range of 30-35 psi (one of many such surveys; the question gets asked frequently, but the answers seem to always be in the same range.)
submitted by a65ragtop