First thing, try changing your fuel filter in case it's getting clogged. The reason it starts up again after sitting a while is that some of the debris can settle back away from the filter media, allowing juuust enough fuel to pass that it starts up and idles okay, maybe even drives a while, before enough debris gets pressed back into the media that it starves again.

If that doesn't resolve it, I've been chasing a similar sporadic issue for a couple years, and have eliminated enough other factors by now that I've got to conclude I must have some sort of chunky debris/deposits drifting around in the tank that occasionally gets sucked up against the fuel intake pipe. Usually I can just shut it off and coast along for a block or so to let the debris drift away from the pipe, then restart and continue on my merry way.

If it keeps dying after a couple rounds of this, I'll make a sharp turn to slosh things around a bit in the tank, and that usually gets it sorted. I've also been filling it up before I get below 1/4 tank lately, which seems to reduce the odds of this happening. Ultimately I'll have to drop the tank and take it to a radiator shop to have it thoroughly cleaned out, maybe apply a sealant if they do that sort of thing or do it myself.

By coincidence, there's a similar story in this month's RockAuto newsletter:

Finally we drained and removed the gas tank, turned it upside down, and out fell a fibrous seal from the cap of a bottle of fuel additive the owner had recently added! Apparently, the seal would float until the gas was low enough that the suction from the fuel pump would suck the seal over the port, shut off the fuel flow and stall the motor. When the suction was relieved, the cap would float back up top until it was sucked back down again. At full tank, it was too far away to be affected by the suction. Once removed the motor ran fine again!