Ok, here is a thought for you. I have this same problem with my truck, but it's not that big of a deal. I just deal with it. Your power wire going from the battery to the starter has a break in it. Mine just clicks, until I get out and move that wire around. Then it fires right up without hesitation. As far as a 0 reading on the solenoid, that only gets power from the switch when you are cranking it over. That should be the reason that it starts sometimes, but not all the time.
Yeah, that's all that's wrong with mine. If it don't start, I just jiggle it a few times. Just enough for it to make contact. I have a new cable, but haven't felt like putting it on yet. Sometimes, those wires corrode in the center (small defects in the insulation, just enough to allow water in) and only allow power to pass through like 1/4 of the wire. Sometimes, moving it (vibration, turns, by hand) can make it make contact enough to work.
That main wire, is hot all the time. Doesn't matter if it's turned to start, run, acc, or off position. If the main cable does not have 12 volts, then it's either bad or the battery is dead. Both of which can be checked with a volt meter.
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