strange, it should have run as long as the relay was switched and sending voltage to the coil....
But, I had something similar. I bought a Challenger that had had a fire under the dash at the ammeter plus it had some rat damage. Having problems accepting ballast resistors on any car today, I switched to the HEI as I consider it to be an improvement over the Mopar box that needs the ballast resistor.
I hot wired the HEI with a relay from the battery and triggered it off the original blue and brown wires. Seemed to work fine but at times the car was hard to start and had to be cranked a bit. Plugs were firing and I could not find a problem. I considered esoteric items such as the starter pulling excessive current and depriving the HEI of voltage while cranking, etc.
Last year, I decided to replace the dash with a set of Autometer gauges and while I was at it, I cut the blue and brown wires under the dash where they come out of the column, tied them together and ran a wire thru the firewall to a terminal block. I then tied in all wiring under the hood that I wanted to be igntion switched to the terminal block.
Car has fired instantly for the past year, hot or cold. I have no clue why it made a difference. I would blame it on the light duty/well aged bulkhead connector if I did not know the plugs were firing prior. Whatever it is, I am much happier than I used to be.
I just hate fixing things and not knowing why