Fuel Tank
From the gas cap to carburetor, the fuel related 1960 parts were made before Ethanol gasoline existed.
If you plan to run today's Ethanol gas (typically E10) then replace it all with parts made for or not affected by Ethanol.
After a month, Ethanol breaks down to component parts and one of them is water.
Fuel additives only delay the inevitable....UNLESS...you religiously drain the month's-old Ethanol from your complete system.
If this is too expensive, buy a back-up carburetor and fuel pump and change your fuel filters often.
If you run all stock parts, like I do, only use non-Ethanol gas.
It's the same with old lawnmowers, chainsaws, weed eaters, tractors, gasoline farm engines etc.
Radiator
A good experienced radiator shop will give you the best advice.
Let them boil and pressure test.