adamsbomb,
Welcome to the Stovebolt. I think Gambitt hit the nail on the head. Your truck probably has a ballast resistor in line before the coil. The system provides full voltage to the coil during START, but when the key is released to the RUN position, power is routed through the resistor.
The typical "It starts, but won't run" scenario is a open, or broken resistor wire, but I think your wiring might have gotten flopped around when the starter was changed.
There are several small terminals on the solenoid, and each has a different function. The 'R' terminal passes voltage to the coil for START, but is dead for RUN. I'm not real familiar with your '62, but I think these wires are not where they belong. Does this sound like a possibility. Someone will be along soon with proper wire color and location...I hope!
Stuart
