I could list so many similar odd problems, I think that it should be a weekly column from readers. Some favorites:
My brother's fiesta would die at random times, seemed random. He said that it started up once when he squeezed a bundle of wires under the dash. After messing with those wires way too much, we found that it was the carb float needle sticking in the bore that would cause starvation.
Again my brother's 67 cougar would idle but stumble terribly much above that. A spare coil hastily connected fixed it. When I connected it all up properly, it had the problem again. Turns out it was a bad tachometer, that when I wired it up permanently I connected the tach which had some kind of short in it.
Last two were on my brother's 57 ford. Straight six, running a little poorly. I noticed that some of the rockers were only moving a little compared to the others. Turns out the lifters are mushroom shaped, and the top broke off a couple of them when they were stuck in the bore and the cam pushed on the edge. Without the top hat they were shorter and barely rubbed on the cam.
More some other time...