Tail Light Problems

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Ok so our left rear tail light is out. I bought a new bulb for it and it worked for about a day but then it went out again. Don't know what the problem could be. Guy at the dealership said it wouldnt' be a fuse. They want like $100 to fix it without even knowing what's wrong. We got pulled over twice in a week cause of it and now we have 10 days to fix it and we have to go to the station to prove it's fixed. Any ideas on what this could be and is it easy to fix? Also when I took the old bulb out there was a lot of rust or gunk inside if that makes a difference.