Bad bulbs, bad switch located either on steering column or on transmission
Try checking the neutral safety switch. This switch is the one in automatic transmissions that makes the backup lights "flip" on when going from park to drive as you go through the gears. When my neutral safety switch shorted my backup lights stayed on constantly.
Is door ajar light on also?
The flashing lights are probably the factory alarm.
What year is the Ford Explorer ? There could be a separate fuse for the lower brake lights
Does the turn signal also blink? If so, you have two wires touching. What happens when you put the vehicle in reverse and the backup light is supposed to come on? If the turn signal lights up and the backup light doesn't, you have the bulbs in the wrong socket.
In the 1988 Nissan the alternator, instrument panel, and backup lights shared a fuse. Before changing a fuse see if the backup lights work (have someone watch when you are in reverse). If the neutral start/backup light switch is broken internally, it can be blowing the fuse when you put the car in reverse.
Either the driver is indication the wrong way or the wiring to the indicators is crossed.
Sounds like the arm and switch in the steering column.
Maybe it is not connected properly or you bought the wrong type of bulb.
Fuse
Really need to know exactly what's wrong with it in order to answer this. You'll handle malfunctioning gauges a bit differently than you would inoperable lights, for example.
Cab lights. Wrong.... Marker lights