Luckily, sitting and meditating on the vagaries of old cars gave the pump enough time to cool down, and some fuel to dribble into the vacuum. Turning the key back on after good rant would allow the pump to blup enough fuel into the carbs to limp home.
Turns out, the tank had run dry years ago and the fuel, combined with whatever fuel additives were in there, had turned into one of the finest varnishes imaginable. The still-liquid gas was several years old, having been added long after the damage was done, put there specifically to fool a gullible MG technician into thinking that the tank was good. You can see the high-tide line of what was about 9 gallons of fuel. Imagine those 9 gallons, evaporated and concentrated into a last gallon or so of muck at the bottom of the tank, and you can understand why the blocked pickup screen was the culprit.
You can just assume that a 40-something-year-old gas tank is going to need to be replaced. MGB tanks rust out from the top due to trapped water around the filler neck. They can also rust out from the inside, from condensation and moisture absorbed into alcohol-laden fuels. I even had one where the tube itself had a rusted hole about halfway up. The car would run fine until it reached half a tank, and than fall on its face as the pump lost siphon and just sucked air.
Update!!! OK, after three of them all in this last year, I am officially recommending that everyone who still has an original tank just roll over and buy a new one. Three cars have come in, all with good original tanks, that would not supply fuel in any reliable quantity. Blame whatever long-chain molecule you may like, but the screens themselves were no longer pervious to fuel. These were clean, non-rusty, no chemical additives or preservatives, good tanks! But something in modern gas is attacking the plastic mesh of the pickup screens and causing them to swell and restrict fuel. Replacement tanks have a much larger mesh pickup screen and seem to behave much better with modern gas. I don't like it any more than you do. We can count ourselves lucky that at least we have reasonably priced replacement tanks available for the asking.