A: It's kind of a rule of thumb that what looks like a fuel problem is actually an electrical problem (or vice-versa). It feels like it electrically fails, so your attention goes to the coil and other potential issues, but it just as likely could be a fuel issue.
I had the exact same experience for a long time and it turned out to be the fuel pump. It was an old one and it seemed to 'vapor lock' under certain conditions. Letting it sit allowed it to bleed-off and it then functioned normally for a time after that. Replacing the pump with the new electronic version of the SU pump has remedied the issue, without recurrence for many for years.
However, I did replace the coil, installed a Pertronix ignition system and the spark plug and coil wires before realizing the actual culprit.
That said if the coil looks pretty with its aluminium case, it can also be bad, so I'd consider changing it for just that reason.
This would be my check sequence:
First, if you haven't, check if you have spark as soon as it dies and won't restart. Pull a wire and and take out a spark plug.
Holding the wire or ceramic top of the plug (do not hold the metal case of the plug unless you want a nasty shock) and ground the metal case of the plug, Have someone turn it over and see if it sparks. If you do, then the coil is not the culprit and I'd move on to the less obvious. If you don't, I'd then check every connection to the coil and all the ignition wire. Include checking the tach lead. They come off or loose, the ignition is defeated and you get no spark.
Next, check if you have fuel right after it fails and won't restart. Pull the hose off either the carb or fuel filter and hold a cup or can under it. Have someone turn the key and see if it clicks and pumps gas. It doesn't, you know where to look next. No clicking from the pump, that's probably the issue. Check electrical connections first, but, if over 10 years old, pulling the pump would be good idea. If the pump is clicking, but there's no fuel at the carbs, it could be a blocked gas line or damaged pick-up in the fuel tank. Fuel flows and you have spark, go on to carbs and their floats.
Another question is - was the tank always low when the car failed? If yes, could be rust in the tank, a damaged fuel pick-up or a partially blocked filter on the pick-up (if so equipped).
I hope that helps you. Keep me posted on how you make out and what you find.
Safety Fast!
Art Isaacs