I had a similar problem, car after complete restoration including having the fuel tank cleaned and coated would on shake down runs would run great for about fifteen minutes and stall. Wait a few minutes, could hear the fuel pump clicking, and then would start and run again for 10-15 minutes. I finally measured the flow into a beaker at the end of the carb inlet hose and was no where near what is is suppose to be. So what was happening was the float bowls were emptying faster that they could be replenished. There was a thread about whether original fuel tanks has a filter on the inlet or not, consensus was they did not, well mine did and I could barely see the pink coating all over it. I bought a new fuel tank, problem solved. Randy Forbes also I believe nailed this as a possible problem.
Thanks
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