2002 Mercury Mountaineer brake lights won't come on

Check fuses
check brake light switch
if you have the 3rd light coming on
suspect and check multifunction switch

may be your brake switch. you can test it with tester, but i do not know your make and model. donate a few bucks for a pro to help, they may help anyway. also check your fuses and make sure both bulbs are good. you should be able to locate the sitch on the brake pedal , push it in and check for hot wires.