Which auto trans? What year is your Bronco?
If a '72 or older, the two Red w/black stripe wires for the backup lights will connect to the same color wires near the base of your steering column under the master cylinder. You can extend them, or you might not need to.
Does not matter which one goes to which, since it's just an open/close switch.
The Red w/blue wires coming off of your switch are just as simple, but will be a little trickier simply because of the greater distance to the pieces they effect.
On the starter relay/solenoid there is a Red w/blue wire (small one on the "S" post) which comes directly from the ignition switch. Somewhere between the ignition switch and the starter relay you need to cut that wire and connect one side to one wire on the safety switch, and the other to the other wire from the switch.
Here again, does not matter which one connects to which, since it simply breaks or makes contact in the circuit.
Doing that will keep your starter from spinning in anything but Park or Neutral.
If your Bronco is a '73 or later model, there is already a square 4-wire plug behind the engine that all these things connect to. When a manual trans is present, the Red w/blue wire side of the plug has a jumper wire, or loop. Either way you'll likely have to fiddle with that connector a bit to make things work with the auto, but it should be pretty straightforward.
Good luck.
Paul