For heading cross or up wind, its just the pressure on the main that does the work. The jib just provides balance and extra drive, so trying to incorporate both sails is adding complication that is not needed. Two lines from the mains boom to the deck edge fairleads, they then cross over on their way to the outer ends of the cross piece of the T shaped tiller arm. The leg of the T is tensioned usually by an elastic to a point somewhere forward on the deck.
If the boat sails further off wind (say to port), the increased pressure on the main causes it to try to move that way, the force is transmitted through the line to the tiller arm and moves the rudder to counteract the turn. As the boat turns toward the wind, equilibrium is restored and the rudder under the influence of the spring, returns to "straight". The crossover is the important bit that makes it work. In use, they always have to be biased for the leg being run – if they deviate too far there is a tendency to gybe round and re-settle to the original course. Part of the learning curve associated with the Braine system.
Vane steering, a different and later system, is the one that doesn't connect to the sails. It uses an airflow direction sensor (the vane) coupled to the rudder, usually involving a gear to achieve the cross over that the system invented by Mr Braine uses to get the logic to right way round.
If using what I assume is the existing tiller arm, extra deck points will be needed to redirect the pull with the arm sited to look like a "real" tiller, i.e., fore-and-aft with the control lines pulling sideways. Braine equipped boats usually have a T shaped tiller arm which sort of simplifies the line layout.