Ignition problem
Remy's got it.
With the factory ECU, the ballast does have a role during start, but since the ignition works with the key in run, its not likely to be the issue.
So here's how the factory diagram shows the ECU wiring was incorporated.
You'll have to tell us whether the insulation color of the wire connecting to the coil positive was changed to brown at this time. it was in '73 but '72 I'm not sure.
Notice the starter switch has two seperate connections for starting. One to the starter relay and one for the ignition.
Even what I've drawn is not quite true. The terminals are not connected together inside the switch, except when the key is held in start.
The point is there can be a good connection to the starter relay and a poor connection to the ignition circuit.