You need you wife or girlfriend or someone to turn the ignition key on and off while you check the voltage at the battery itself, and then going away from the battery to the chassis on the negative side and if ok those two places, go from chassis ground to the hot lead down the line from the battery toward the load. It must be either that the battery voltage drops under load, or that there is a high resistance somewhere in the circuit. You get to play Dick Tracy to find it.