My guess is its a regulator problem
voltage at the battery with alternator chargeing should be 14.5 volts
voltage at battery with alternator not chargeing should be approx 12 volts
to trigger the regulator into switching alternator in to charge mode switch on headlamps and heater motor and bring revs up to 1500-2000
if your regulator doesn't work right you could boil your battery and (but not as a consequnce of a hot battery) the voltage measuerd at the battery will be higher than 14.5 volts when the alternator is doing its thang
dash lights probably don't like an over voltage, bigger voltage pushes more current through the bulbs and burns em out
regulators come in two types, mechanical (you can adjust these by dudicous bending or screw twiddleing depending on model)
or just give it a good thump with a small hammer. it has a mechanical armature that is responsible for swicthing the current to the coils in the alternator. a good thump often loosens this if its got stuck
mechanical regualtors are supposed to be set up for the temperature of the climate the car will spend most of its life.
i.e in cold temps you usualy set em up to give a higher voltage at the battery when the alternator is chargeing and the reverse for hotter climate.
or solid state. you can buy em off Mopar performamnce or other suppliers, however i think you need to get one that isn't 'Race only'
i.e it should be the one that works with their electronic ignitions (Blue orange, chrome box) for street use
otherwise blowing bulbs can be put down to excessivly hard shock absorbers on a very low car
or if your dash lights are supposed to have a variable supply to allow dimming has someone bypassed it?