Your Explorer should be very similar to my Ranger. As with most vehicles there are essentially three lights on the rear. Park lights (come on with the headlights), Brake lights, Reverse (or Back Up lights). On some vehicles one Brake light bulb is employed to flash for turn signals but instead of that, a separate turn signal bulb can be used usually when there are amber rear turn signals. I'll take a moment to consult the wiring diagram for your vehicle to be sure. Ok, yours has Rear Turn / Stop / Park lamps. Those are a two filament bulb (like two bulbs in one glass envelope, one is brighter than the other). The filament that is less bright is for the Park lights only. The other filament in that same bulb is both your Turn signal and Brake light. One filament can go bad but the other still works. As a rule of thumb brighter bulbs tend to burn out faster. If the left brake light goes out you won't have a left turn signal either. Likewise with the right. If both of those brighter filaments go out, you have no Brake lights and you will have no Turn signals in the back.
If I'm correct to access the bulbs you probably need to open the liftgate and look for screws that go in from the inside toward the lenses (2 or 3 of them) that hold the lenses in place. The bulbs are push-and-turn to lock in rubber plugs. Free the lenses and inspect the bulbs. The one you are concerned with has three wires going to that particular bulb. The other bulb has only two wires, that one is the reverse light). Take the three wire bulb out and see if it is blackened inside. If it is then it is bad. If you cannot tell then take the bulbs to your local auto parts store and ask them to check them. A quick test is to check the turn signals which you can test both at the same time by turning on your Hazard or "Emergency" flashers. They operate both those filaments together, as it is essentially flashing Brake lights. You can also turn the ignition switch to the Run position and turn on each turn signal and go back and check. Let us know what you find out.
Consult your owners manual if you have one on how to remove the bulb from it's socket. Some you just pull straight out while others you have to push down on and turn the bulb slightly to one side to be able to pull them out.
Here is nice little YouTube video showing how to get to the bulbs on a 99 Explorer which should be similar.
http://www.youtube.com/watch?v=Ep5BbFJsJTU
Note the bulb he takes out in the newer pull straight out type while my 93 Ranger has the Push down, turn, and then pull out older style bulbs. Your Explorer could have either so check the owners manual for bulb replacement to be sure which type you have.
