Spyke,
I've had the same thing happen to my '03. Read about it on here, also.
For me, the fix is to take the bulbs out of the rear-left tail light assembly. I clean-up the connectors with the eraser on a pencil & apply an electric grease that cuts down on the oxidation on the contact points. Can't remember what they call the product. I think they call it "di-electric grease".
So far, it has taken care of the problem for a couple of months, at a time. Then it comes back. I just did it again, last Friday, for the third time in about six months.
The "chime", along with the "lamp-out" indicator will drive you nuts. That damn chime will sound-off ten to fifteen times, in a row & then stop for a few minutes. Then it will start-up again, a bit later.
BTW, I've never had any "bad" bulbs, in my truck. I'm getting tired of all the "crap" on these trucks that are supposed to make our lives better. The only problem with my truck is the "warning device", itself!!! What a piece of junk.
Good luck fixing your problem.
Joe F. (Buffalo)