Both of my brake indicator lights came on just the other day. Sure enough both of my brakes lights are not working however I think it's very odd that both lights went out at the same time? Has any one ever heard of this or had this happen?
Since we don't even know what car you're discussing, anyone's guess is as good as anyone else's. I'll vote for a backup-light switch failure, having nothing else to go on. You didn't even tell us if the bulbs were bad or not.
I can only assume it's an 2001 E46 330i based on his username... I heard E46's have some kind of grounding issue with the tailight assemblies. You might want to see if the grounds are sufficient.
if it is an e36 they have a brake light switch that can break over time it is a very cheap and easy replacement, the job takes all of 10 minutes
I couldn't tell you the amount of those grounds that I have fixed on those e46's. But I also have seen both bulbs go out before. Not unheard of but doesn't happen offten. If it is just the bulbs, remember to use the nickle base bulbs or they will cause problems.