It takes current to operate the starter, which pulls down battery VOLTAGE making the spark from a defective ignition system too weak to light off the charge in the cylinders.
When you release the starter button, battery voltage rises, and the engine is still turning over (on it"s way to coasting to a stop) and fires from the now "hotter" spark.
You may have a weak ("fried") coil, damaged from TOO LITTLE primary resistance in the primary circuit and/or from the key being left on with the engine stalled, or, on the other hand, the coil may be OK, and there is TOO MUCH resistance in the primary circuit, casing low primary current/low spark VOLTAGE.
There are/have been coils with various primary resistances on the market and each individual doing a 12Volt conversion may opt for a slightly different way of doing things!
This makes for a lot of FUN when a later owner has problems.
You MAY have to start over with a new coil and appropriate primary resistance. here has been enough written about this to fill a book, over at the "N"-specific Board. You may want to surf over there.