350CID, HEI
78amp alternator tests fine, volt and amp output
Battery load tested weak
Truck idles fine with or without electrical load, while driving at any speed as soon as ANY load such as headlights or AC are turned on truck loses power dramatically, but responds when you hammer down on the pedal, dash gauge is reading well under 12 and is slow moving up or down, retest alt output to verify dash gauge and output at alternator reads normal, WTF??
suggestions

 

Do you have a really low idle? That might cause that. Had a k5 that idled at 500 and with the heat all the way up the volts would drop way down

 

x2, try bumping up the idle a little and see what you get, theres a little screw on the thing that rotates on the carb that you can turn that will set how far it can turn backwards - idle screw... Should idle around 700-750