First check the fuel tank, invariably in old cars it is made from pressed steel and is subject to corrosion especially where straps or fixings are. Give it a good look over for any bubbles or spots that look damp/dark and check to see if the fuel gauge moves much at regular intervals when the car is parked up. Next check the pipework, again many cars had steel pipes with later replacements being copper or plastic (plastic being particularly vulnerable from hot exhaust pipes as many manufactures ran the two pipes close to each other!)
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