Back Brakes won't bleed
Good advice from other members. My opinion is either a collapsed rear brake hose at the differential or try removing the rear bleeder screws from the wheel cylinders and run a wire through the hole. Or the bleeder screws could also be plugged. My 72 Dart has a self centering pressure differential switch. your 71 probably does too, so I doubt that is the problem. (the brake warning light on the dash would be on). The brake light switch should not be related. I have been a brake mechanic for 40 years.