I need to add that it only loses that 1v with the engine running. With the engine off and key on the blue wire at voltage regulator,ballast resistor is the same as battery voltage.
You may not have enough (or any) load on the circuit with the engine off. THIS IS your problem if you have measured that drop at those two points. You just need to figure out where it is materializing.
You already jumpered across it and proved the voltage went back down, so you are in the right area.