sounds like bad break light switch. your break pedal has a switch that turns on your break lights when you press on your breaks and off when you take your foot off the pedal.
check brake light switch
If your brake light is not coming on, you might have blown a fuse. You might also have a bulb that is no longer working.
Check the bulb.
most likely a bulb b/c if it was the fuse your other brake and signal light wouldn't work... most vehicles the brake and signal light are all in one bulb... try replacing the light bulb
Have you checked your bulbs ? The tail light / brake light bulb has 2 wires inside it In my case I have had to change each bulb because the brake light portion did not work but the tail light portion of the bulb did ( I'm assuming that your front park lights are working )
There are likely one of two reasons why a brake light on a Brava is not working. Either the bulb is burned out or a fuse is blown.
The Turn Signal and Brake Light may be operating from the same Bulb, or separate bulbs. Regardless, the Brake light filament must be burned out. Another option is that the Brake Light Circuit is on a separate Fuse, and the Fuse is blown. Check for those possibilities.
the fuse should be for all brake lights and tail lights if only one is out its a bulb
check your bulb and fuse
Could be a short in the brake light switch or a bad bulb.Try removing all of the tail light/brake light bulbs and step on the brake pedal to see if the fuse still blows.If it does it is a brake light switch problem or a short in the wire harness.If not it's a bad bulb.
If all have failed possible fuse or brake light switch If only one has failed bulb or wiring to that fixture only
bulb # for brake light on your explorer is a 3157 backup light bulb # is 3156 hope this helps