I have a bradley / Alko combnination, and the "double dunt" on the handbrake puzzled me for the first couple of times.... then I read the instructions!
This is how mine works, but the theory applies to them all:
The initial rise just tensions the gubbins in the drum - there is an over centre cam , because the hitch will only apply the brakes in forwards (due to the "sliding" shoe in the hub) - the hitch has an end stop roughly equal to the end of the "fast" bit of the handbrake. At that point it's simply tensioning everything up & applying the fixed shoes- hence the rapid rise with spring. There is an over centre cam that will allow the lever to go even further - this takes up the slack created when the trailer rolls backwards abd basically overrides the auto reverse. if, however it's moving (even slightly) as you pull it, the revere shoes never grip so it goes all the way, assisted by a big old spring....
I have to unhitch on a downhill t get it back in the garage. If I don't get out, put the brake on, then rol lthe car back 4" I canlt lift the hitch off the ball due to the weight. When / if I do, it rolls back about 4" before the lever springs up & it stops.
Not maybe one of my better techy explaations, but hope it helps understand what's going on in there......