Tire pressure for a 1962 Valiant with 14" tires

No, sir. Running max allowable pressure amounts to functionally overinflating the tires, and the result will be much faster and worse wear in the middle of the tread.

OP, if you want to be scientific about it, use chalk. If you can't be arsed, pick your favourite number between 32 and 35 and keep that number of PSI in all four tires; you won't be far off from optimal.
Thanks, Dan! I've seen "the chalk method" mentioned several time, but that's something I've actually never done. I would just "guess" you color the tread with chalk and run over pavement to see the tire's contact patch, but I'm not sure. Can you expound on it?