Wire wound resistors (Ballast resistors are wire wound resistors) can open after it warms up (due to current flowing through it) and after it cools it can make contact again (internally) and pass the voltage through to the coil.
Exactly, and it would be really easy to diagnose.
When it won't start just jumper the coil to the battery and I bet it starts.
(easier to just replace the resistor though probably)