Your ignition (and the engine bay) only has ONE "run" wire coming from the ignition switch, through the bulkhead........."run" or IGN1......AND IT GOES COLD during cranking
The original Mopar wiring has IGN2 ........normally brown......which goes from a contact on the ign switch out to the coil+ side of the ballast IT IS HOT IN START.
You must hook those two together.
CONSIDER cutting the blue where it comes out of the bulkhead connector, and putting a relay in there to handle underhood loads
Also BEFORE you do this, CHECK your running/ charging voltage at the battery. If it is much above 14V you need FIX that as it is likely due to voltage drop in the harness/ terminals/ etc