73 duster Emergency brake?

Mopars are rear brake happy, they ALWAYS were with the factory disk front/drum rear. The factory prop valve does not at all make it impossible to lock up the rear brakes, not even close.

The rear drum adjusters advance when the car is traveling in reverse, that's when the adjusters tighten up to keep the rear brakes adjusted.

If you're not reversing in a straight line, one adjuster can adjust more than the other one (because one wheel is traveling further). I found this out myself because I used to park in such a way that I always backed while turning the same direction. This would result in one rear wheel adjusting slightly more frequently than the other, and when that would happen it would lock one rear wheel before the other. The brakes were wearing at the same rate, it just took more time for one of the rear wheels to travel the requisite distance because I was always turning while backing up. This is one advantage that disk brakes have, as they wear they maintain their adjustment constantly. Older drum brakes didn't self adjust at all, you had to do that yourself. The self adjusting brakes on these cars were an improvement, but, they rely on the adjusters and the adjustment is only as fine as the star wheel- so the adjustment of the brakes does vary and can be different side to side because the adjusters are independent of each other.

The adjusters should only be adjusting as the brakes wear. So it shouldn't be something that happens all the time, especially if you just did the brakes, put the adjusters on, and set the adjustment.

Since none of that stuff was hooked up before, it's most likely that something with the adjusters isn't hooked up properly. That's made more so by the fact that the emergency brake isn't hooked up, since it is part of that system even if the brakes should work properly without it being hooked up.