Lighted SPST switch waiting problems
two possibilities .
your circuit looks fine . have you connected to the correct terminals on the switches ?
Or it could be that your battery is too small . In that case the igniter would draw so much current that the battery voltage falls too low to ignite or light the LEDs. I would monitor the battery voltage with a multimeter whilst operating the switches. I assume that the LEDs have an internal resistor . If they do not you will need to add series resistors of around 1K.