Sounds like it could be the turn signal switch but that is often located inside the steering colume. They dont' often fail but can. Its not an easy job to replace that for the novice. Might be best to consult a qualified ASE shop or a GM dealer.
The thing to keep in mind with your problem and that of the 1st poster is that other things could cause the same symptons and it should be checked out before replacing parts to avoid unnecessary expense.
Fyi - Trailer wiring harness are often the cause of many of these problems. They are often installed poorly.