I've got a similar issue, still happens even after installing the Weber and electric pump, new fuel filter and plugs/wires/cap/rotor/coil. Also just rebuilt the dizzy with fresh thermal compound under that ICM, which the PO had already recently replaced when I bought it, perhaps chasing the same issue as the old ICM was in the glovebox with a note on it saying "maybe still good?"
It doesn't just die completely all at once but, rather, just starts to kinda bog down and then drops to idle and stays there, no matter how much I goose the throttle, before finally dying. However, I also don't have to let it sit before restarting; I can usually just declutch to keep coasting along, and once the engine stops turning, I can usually just restart it right away while still coasting and continue on my way.
At this point, I'm suspecting a chunk of rust/debris in the gas tank may be getting sucked into/against the fuel pickup, starving it for fuel. Until I can remove the tank to get it cleaned out and maybe sealed, I'm gonna try affixing a strong magnet at a bottom corner of the tank to draw any rust chunks away from the fuel pickup. Got a thumb-sized neodymium one I salvaged from an old desktop hard drive that oughta do the trick.
There could also be a fault in the two-way vapor valve near the tank, allowing a vacuum to build up in the tank that could impede fuel pickup. This valve should divert positive vapor pressure to the charcoal canister underhood but allow ambient air into the tank as fuel gets consumed.
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