The resistance wire is fed by the key switch ignition terminal which also feeds the fuse panel cluster fuse. You could have a poor connection on the key switch terminal causing the voltage drop enough to kill the ignition yet not enough to affect the gauges in the cluster. I would check the voltage at the cluster fuse just like you did at the ignition coil and see if you get the drop there. If you do then I would suspect the ignition switch connection. This is a common thing that happens on these old harnesses.
The ignition coil feed (pink wire) also goes directly to the firewall block inside the cab behind the fuse panel. It connects there with the resistor wire which joins the two yellow wires as you have discovered. The yellow wire on the R terminal at the solenoid shunts 12 volts from the battery to the coil as soon as the starter engages, and it disengages as soon as the key is released. This is for a full 12 volts to the coil for cold starts, and it is why the engine dies as soon as you release the key. These connections at the firewall block also corrode and cause increased resistance which leads to voltage drops.
The other yellow wire goes to the coil for 8/9 volts to the coil for normal engine running. This prevents coil burnout and protects the points from arcing and failing prematurely. The resistance wire was originally an orange white purple cloth covered wire which fades over time as yours has. The diagram below shows the wiring path.
Here is the ignition switch wiring. The 12 gauge pink wire is the ignition wire.
Here is the wiring showing the ignition wire going to the firewall block and the fuse panel.
You should also check the output of the alternator to be sure it is providing the right amount of voltage at all times. The battery should keep the ignition running even if the alternator output is low, but is can't hurt to check it.
Three of the best mods we can do to our old trucks is, Converting to an internally regulated alternator, HEI ignition. and headlight relays. These are very easy and relatively cheap to do. There are tons of how to s. on this forum to help.
If you want a test of the resistance wire just get a 1.8 ohm ballast resistor from the auto parts guys and run it in series with a wire from the fuse panel IGN UNfused terminal to the positive side of the coil. You can leave the other wire on or run a new wire from the starter R terminal.