I had the same problem here recently. This is a reply I got on another forum:
"It's the turn signal/brake light relay. If it's buzzing, it stops when either the brake pedal is applied, or turn signals are on. But, the issue isn't the relay itself - it's the turn signal lever, which gets dirt inside. The intermittent short drives the relay crazy. The true fix is a new turn signal post/switch, which if I recall, comes in over $100. For me, I sprayed the living hell out of it with contact cleaner, which "fixed" it for over a year. It only now just started up again. I'll attempt the same, but the real fix is a new turn signal post/lever/switch assembly."
After a few days of hearing it, I got an air hose and sprayed air into the turn signal lever and steering column and up under the dash. I don't know if this helped, but the noise stopped a couple days later and I haven't heard it since! This was almost 2 months ago.
