Do it yourself, change the right tail light on your Ford Explorer made in the years 2001, 2002, 2003, 2004 or 2005. For this repair you will require a Phillips screwdriver. It should not take longer than 15 minutes, because the process is fairly simple.
First of all, open the back door of your trunk and look on the right side, near the tail light, after two Phillips screws (marked with red circles in the picture below). These are the screws that actually hold the tail light assembly. You should unscrew them without much effort, using the Phillips screwdriver.
At this point you can basically detach the assembly by pulling it towards you. Be careful, because it has mounting studs on the back, right extremity and they can be tricky. Pull the assembly firmly and it will eventually pop out. Then, you will notice the two electrical harness shown below, that you will have to unplug, if you wish to remove the assembly.
If you just need to service the light bulbs, rotate their sockets counterclockwise. After you finish all the repairs, make sure you reinstall everything back together as it should be and remember not to over tight the bolts of the tail light, as you might brake the plastics. This is all you need to do, in order to change the tail light on your Ford Explorer manufactured between the years 2001 and 2005.