Yes, your second and third pics show the coil.
It's been ages since I had a truck with a coil, but wouldn't there be two wires (one resistance or with ballast resistor, and another without) on one of the coil terminals? I seem to remember that. I had an issue with that last truck and went as far as replacing the resistance wire only to find out it wasn't the problem.
The ignition switch may also be at fault. If the "Run" contact is messed up, it would cause a similar issue. The wire going to the coil from the switch should be hot with the key in either "Start" or "Run" position.
