I also experienced this on my 04. Went to use the turn signals, and nothing. Then a few minutes later, everything back to normal. The first time is was raining, but the next time it was dry. Is there a TSB on this?
I experienced this driving my '04 CTS through the mountains of West Virginia during a rainstorm a couple months ago. They just quit working. Then started working again just as suddenly. No problems since.
I used the turn signal like everyone does, but nothing happened. Tried the other direction, nothing. Then a few minutes later they are working again. Hope I never get pulled over for not using my turn signals and try explaining that!