1999 Pontiac Grand Am dead battery

Electrical problem
1999 Pontiac Grand Am 6 cyl Wheel Drive Type unknown Automatic 140000 miles

the rear driver side light keeps going out. I tried to replace the bulb but it still goes out. If I hit the light with my hand it'll come back on. Do you think there is a wiring problem or do I need a new battery. It seems like something is killing my battery. There is a wierd smell like a rotten egg coming from the engine. There is also different lights on the dash that go off and on like the brake, abs, the battery and theft lock