I had a similar experience with a 1965 Rambler. I had replaced the coil wire (the high voltage wire between the distributor cap and the coil) with a resistance wire that was defective. I was trying to get rid of the ignition noise in the radio. It will only take a couple of seconds, but substitute another coil wire and see what happens.
If you are getting 6VDC on the - side of the coil with the engine not running, ignition on, points closed, then there is a problem with the grounding of the distributor. You should get 0VDC under those conditions, 12VDC when the points are open. You should get 6VDC on the - terminal of the coil with the engine running or cranking.
Is there the possibility that the condenser wire terminal is on the wrong side of the terminal block, it must be in contact with the points spring and - coil wire. You also have to check very carefully that none of these wires get pinched anywhere as the distributor turns. also check closely where the coil wire enters the distributor that you don’t pinch it when you replace the cap.
Just to cover the basics, the point gap is measured at the top of the cam lobes in the distributor. When adjusted correctly, wiggle the top of the distributor shaft and see if the gap changes significantly (visibly without the use of a feeler gauge to tell). The timing order is stamped on the head or block somewhere, identify the #1 post and see that the rest of the wires follow the same sequence. It is best if you have a book that shows the correct spark plug wire diagram.
I’m rooting for the OP to get this Chevy C-10 running smooth as silk again. I’ve always liked the body styling in those years on that model of truck, so I hope it can be returned to the road for all to see a appreciate. And those C-10’s were tough, reliable trucks.
When I was a kid in Colorado one of the families that attended the same church had a C-10, and we kids discovered that the key to one of our trucks also fit that same C-10, so we’d sneak out into the parking lot and start up that old C-10 and sit in the cab to keep warm, in order to avoid attending (what we considered to be) the not-so-interesting church sessions. I have to say the discussions we had sitting in the C-10 were probably a lot more interesting than those going on inside the church.
Keith is right, the negative side of the coil (the one that goes directly to the points) should be close to 0 volts when the points are closed. It has to be that way if you think about it, the points are just a switch and they switch the negative end of the coil to ground when (statically) closed. On the positive side of the coil , there might be a ballast resistor between the battery and the coil, so the positive side might indeed be 6 volts when the points are (statically) grounded. That would be the case if the ballast resistor is the same as the coil resistance. The positive side of the coil would be close to battery voltage when the points are open.
Setting the point gap exactly isn’t very critical. Engines of this vintage would run over a large range of point gaps. It’s just that as the gap changes compared to spec, the ignition timing also changes. OP might try an experiment, turning the distributer a bit, this way and that, see if the engine can be made to run better. Could provide a clue to what is going on.