Two wires, pink and white.
Assuming you have the standard-duty switch (most cars do), it looks like this:
One wire connects right at the collar at the base of the switch plunger, the other connects on the back of the switch (pointing rearward toward the back of the car). The switch works like a refrigerator door light switch: when you push the brake pedal, the plunger extends by spring-load, completing the circuit and turning on the brake lights. If your switch doesn't do that, replace it (it's not expensive
). The heavy-duty switch has both terminals at the back, and looks like this:
I like these better because they're easier to adjust, and it also happens to be less expensive
If your brake light switch is okeh, though, and there's no broken or disconnected wire, the problem is in your turn signal switch. On cars with combination brake/turn lights like most of ours, the brake light power goes through
the turn signal switch; that's how the one light/two functions magic is done. If you need a new turn signal switch, shop carefully; most of what's on the market is poorly-made junk from China. See here
While you're paying attention to your brake lights...remove and clean the lenses in hot soapy water. If the reflectors are at all dull or peeling, stuff wads of masking tape in the bulb holes (or remove the sockets if they're the removable type), clean the reflectors with alcohol, then spray them with readily available "chrome" spray paint, which is practically ideal for the task.
Then put in these bulbs
(the white ones for the back-up lights are these
To run these properly you will need to swap in this turn signal flasher
(2-prong like original, direct swap).
Also note these recommendations are not random -- they are the only legitimate LED retrofit bulbs. There's a mountain of garbage on the market, too, so use _only_ these specific LED bulbs; more info here