Sounds to me like it's willing to run ("fire") until you release the key, correct? But as soon as you release the key as the engine catches, it dies. Am I right in this assumption?

If so, your problem probably lies in circuit 16A of your diagram. Here's what things do:

Find wire 16 that runs from the coil. It goes to the bulkhead disconnect and is spliced to wire 262 at the disconnect. When you hold the key to START, 12V goes down wire 262, onto wire 16 and then to the coil, to provide power while cranking the engine. 12V directly at the coil gives you a good, hot spark during engine start.

When you release the key to RUN, the starter solenoid drops out and there is no longer 12 volts on wire 262. This takes the 12 volts off of the coil.

But without power to the coil, the engine won't continue to run. So...

With the ignition key in the RUN position, 12 volts goes through wire 297 from the ignition switch (which somehow becomes wire 16 again if you follow the line). Anyway, this 12 volts goes to a disconnect plug and to the resistor (right side of the drawing). From the resistor, wire 16A connects power up to the firewall disconnect, through the pins in the disconnect, into wire 16 and back to the coil. The resistor (or resistor wire) is designed to reduce current flow to the coil during normal running to prevent coil burnout (something that will happen to a stock coil in fairly short order if you always have 12 volts to it; not to mention the damage it'll cause to your points and condenser).

If you have a problem between your ignition switch and the firewall disconnect, it will cause those symptoms.

I'd start by wiggling the firewall disconnect on both the inside and outside of the firewall. If the problem goes away, or changes, you've located the fault. Likewise, you can shake the wires around inside the car between the ignition switch and the firewall disconnect.

Good luck.