Late, but answering because others might read this afterwards.
On the 3cIII it shares the same brakes with the leyland tractor skid jcb used.
There is a central shaft from the axle, which rotates two friction discs with splined centres onto it, and between the two is a actuator mechanism with flat sides which forces the two discs onto the inner and outer casings.
The actuator is two solid thick discs with ball bearings running on ramps between them, and joined by a linkage which contra rotates them. So when you hit the brakes, they contra rotate, ride up the ball tracks and force the discs into the stationary elements. Sort of like a conventional clutch but in reverse action.
To retract the brakes, there are 3 or 4 springs, these pull the actuator halves back together when the mechanism is released. I would guess that either one of these springs has become misplaced or broken or the actual splined shaft the friction discs run on has become notched/corroded with age, and the act of reversing puts a different unworn face of the shaft into play so that the mechanism can retract without stiction, or releases tension so the remaining springs can retract.
The best and easiest method to see which is to strip them which you have to do to fix in either case.
For this, remove the throttle cable, and go underneath and remove anything else which will prevent the floor plates being lifted. Then remove the 8 or so bolts holding the floor plates out and lift them out the way.
You can then remove the two brake covers on either side exposed by this action and disconnect the linkage and fish the innards out. It may be that dirt and corrosion stops the parts sliding freely, in which case a flat bar with a small hook bent on the end helps considerably in this action.
Exposed, in the light of the day it'll be easy to spot what is broken or requires lubrication. Its probably about a afternoons solid work to strip it all out, clean it and rebuild.
Im at the lubricating stage right now on mine. Hence its very fresh in my mind...
Phil P, September 2010