The Boot backup light does not work on 2002 ford focus SE. I checked all wires with a voltage checker there is fire on both sides but no voltage in the light on the lift gate. Is this a fuse problem?

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You can see the fuses, not only check the fuse, check for voltage on fuse circuit, use a test light, goes hot with key on.
On the hinge side of driver door, check the wiring harness. Probably has a protective rubber boot covering, see if you can pull the boot back far enough to get at the proper color. Green wire with blue tracer should be voltage, with key on, use a test light. Also, check the ground wire, it is black. You can use a test light to check ground also. One end of test light touches battery voltage, the other end penetrates that black wire, if the light comes on, the ground is good enough for test light. The driver door is opened and closed so much, sometimes the wires break. If you make a hole in the wire, use finger-nail polish or something to cover the hole.

I would start at the headlight switch check your ground wires and connections at the light themselves also check the bright dim switch

Could be in your signal switch..Get someone to watch your brake lights,,and apply your brakes,,and move your blinker switch around and see if the brake light tries to come on..The brake light circuit runs through the switch...Even if the blinkers work it can have a short in the switch,...Then if that dont work,,take a test light and see if your getting voltage to the light...If so wiggle the wires on the light socket and see if there is a bad connection

Broken wire where trunk lid opens

If bulbs are definetly ok you can look behind trim on the left side in the boot, which covers the space between the boot floor and the window, you are looking for a green/red wire in a connector. this is the power cable which supplies both rear side mounted brake lights. You should check for voltage at this wire when pedal depressed. If no voltage you would need to trace this back to where the wire is joined in the loom as it feeds off the wire which supplies the high mounted brake light and you have stated that this works. Would still double check bulbs first though if you did'nt replace them. Hope this helps.

try changing both bulbs, but watch as the stop and tail light bulb can only go in one way seen it loads of times

2.0L SOHC
2.0L DOHC

On the left inside the boot behind the carpet is a blue connector, this has all of the wires for the rear lights. if you use a test lamp you can identify which wires do what and connect as you go. Use a self tapping screw for earth.

sounds like defective alternator. ck output voltage on back of alt. should be 13.25 or more

I'd backtrack with test light from socket with low voltage reading. If you probe behind socket, or wire going into socket for power, and it shows bright, you've isolated problem area.