Brake light question

My 1999 Jeep Grand Cherokee would not start yesterday. I lost all power..I checked my battery connection and found that my positive cable was a little loose and dirty. I moved it around a bit and tightened it up some and it started up just fine. Today I was on my way to work and someone told me that my right brake light was out. Does this sound related? Fuse problem or bulb? I've been told that I need to locate a 10 amp red fuse? Should I be checking the bulb before I go looking for the fuse? How can I tell if the fuse is bad once I locate it and is it difficult to remove the plastic caseing to get to the bulb?

THANKS!!