I am in agreement with the reverse flow pump. The thermostat would normally see hot water coming from the engine and stay open, once opened. If the water is coming from the radiator, the thermostat would cool down again and close.
Jegs sells aluminum pumps that are made to replace conventional pumps, but are reversed to be used with aftermarket serpentine setups.
Chevy pickups did not get the 350 until '71. What year 350 do you think you have?
It wouldn't be the first time a part got put in the wrong box.