On a Chevy, the light switch has separate terminals for the front and rear lighting. Not to mention, it COULD have separate fuses and relays as well. IF you go to Autozone.com, you can type in the vehicle and there are wiring diagrams free on their site. I got extras off there for my 89 Suburban.
More than likely, it's one of the following: Faulty light switch, broken wiring, shorted wiring, bad turn signal switch in column, or bad or shorted trailer plug (if it has one). Also, like I said earlier, possibly a bad fuse or relay.