On engines with distributors and a single coil there is a separate START wire and RUN wire for the coil.
Symptom of one of these circuits failing is either engine starts while cranking(START) then dies when key is back in RUN position.
Or engine doesn't start while cranking but fires as soon as key is back in RUN, i.e. engine is still turning when key is back in RUN position and coil sparks, your description of "bumping the key" to get startup reads like this is the problem.
Single coils only need about 8 volts to generate a good spark without overheating, vehicle electric systems are at 13.5volts when running, so will shorten the life of a coil.
The RUN circuit will have a resistor to lower the voltage at the coil from 13.5 volts to 8volts.
When starting the engine the battery voltage will drop to about 10volts(starter motor cranking)
With the resistor in place the coil only gets about 5 volts so very weak spark.
So they have a separate START power wire for the coil, this can be thru the ignition switch or from the starter relay on the inner fender.
It was the "I" post on the 4 post starter relays.
When engine is cranking the coil gets the "10volts" directly, no resistor, so has a hotter spark for starting cold(or warm) engine, but just while cranking.
To test if this START circuit is the problem, put a jumper wire from Battery + to the + terminal on the coil.
Start engine
If it fires right up then that was/is the issue.
You can trace the circuit to find the issue, best way..............or you can add your own START circuit.
You need a length of wire and a diode
On the 3 post starter relay there will be a large wire that goes to the Starter Motor, this wire only has voltage when engine is cranking, you will need to attach your wire to that post.
That wire will go to the + terminal on the coil, BUT....it needs a diode so the RUN 8volts(also attached to the + coil) doesn't run backwards thru your new wire to the starter motor.
Diodes are cheap, they allow power to flow in only 1 direction, a diode will have a line on one end, that "line end" will go to the + on the coil.
You can place the diode at the Starter relay end or the coil end of your wire, but the "line end" needs to be hooked to the + on the coil.