I'm totally confused now. Which controller do you want to use? The Bighit controller has an orange wire, which goes to your ignition switch and battery meter. The diagram isn't very clear, but it should be the same as any standard Chinese controller and so the orange has to be connected to battery voltage (36v) via the switch, and when the switch is on, the battery indicator lights light up. In the diagram, it shows 36v (DC+) coming out the controller to the switch and going back down the orange. That red wire must be connected to the thick red inside the controller via the internal wiring. The 36v is also used for the 36v riding lights
I can't see your no name controller diagram because I don't have MS Word, but from you description, it's the same as usual:
There should be three wire for power (thick red; thick black; thin red, orange or pink). The thin wire has to be powered with battery voltage (36v) to activate the controller. Easiest explanation is like this: Connect it directly to the battery; cut it in the middle; send each end to a switch; then connect the battery indicator light wire to the controller side of the switch. Then your indicator lights will come on when the controller is activated and vice versa. If you connect the indicator lights to the battery side of the switch, they'll be on all the time your battery is on.
The brakes on your bike are standard 2-wire brake switches that simply join the two wire when you apply the brake. There are two wires connected to the Bighit controller: one is 0V (black) and the other is the return (yellow) that pulls a pad on the pcb down to 0v and tells the controller logic to stop power. No name controllers usually have black and yellow wires as well, but could be any colour. There's not usually any other two-wire connectors so you know which ones are for the brakes. Sometimes there's only one two way connector on the controller, so you have to splice your brake wires together in parallel so that you have an either/or situation. It doesn't matter which way round the wires go because it's only a switch.