Thanks everyone for the suggestions and advice. I followed your links and found that my GF's X5 had a right lower taillight metal socket with a hole in the metal due to electrolysis at one of the contact points where one of the light bulb prongs touches the metal socket. The plastic underneath the affected metal socket was also moderately melted, such that is bowed backward.

Solution: I cleaned the corroded metal with acetone, sanded the corrosion away with 1500 grit sand paper, cleaned it again with acetone, and then soldered the hole in with solder metal and then put a healthy amount of solder on the side of socket that was bowed backward to fill in the gap caused by the bowed plastic. I then sanded the solder smooth with 60 grit sand paper and took needle nose pliers and lifted the prongs of the right lower light bulb to make sure a more secure metal-on-metal contact occurred. Finally, I coated the contact points of the repaired socket and the prongs of light bulb with dielectric grease from Advanced Auto to prevent future corrosion or possible open circuit electrolysis.

Total cost: $1.29 for the dielectric grease + borrowed a solder gun from a friend + 15 minutes total labor time

Result: Works like new!!!