The Multi-function switch( turn signals,hazard,lo/hi beam,cruise control,windshield wipers/washer) has deteriorated inside and one of the thin metal contacts has worn out or come loose. Replacing this assembly should fix you up. The service manual for the 1999 says to remove the air bag ,steering wheel and ignition switch to perform this operation, however I did change the one in my Suburban without removing any of this. You can buy an aftermarket switch for less than half of what the dealer gets. Of course the quality of the part may be questionable and it's a real pain to think you might have to remove and replace it again for some other problem( like cruise control shuts off when the right turn signal is engaged ; mine does ,so I live with it!) Definitely somewhat expensive and troublesome for a nuisance fault!
If they turn on but don't blink, you probably need to replace the signal flasher relay.
Turn signal switch is melting...replace the turn signal switch in the steering column.
It could be a faulty ground wire.
The turn signal flasher is what makes the noise and lets the turn signal flash.
your problem could be in the switch its self. unfortunetly they are expensive to replace, i had to actually wire a switch direct to the blinker system.
Could be the control stick for the blinkers. If the lights work, try replacing the stick or checking out the signal path for that blinker
the turn signal switch sends current to the turn signal flasher. it then goes to the bulb. The turn signal switch will turn on the turn signal and when the brake is applied it cancels out the brake light as it is a duel element bulb. 1 element is for brake and turn and the other is for parking lights. you can not have a blinker and a constant feed to the same element of the bulb at the same time.
The brake lights and signal lights are tied together in the signal switch, also known as the "multifunction switch".
Problem most likely is in the Turn Signal switch. I had same problem , replaced Turn Signal switch assembly and that fixed it.
often the blinker is made to blink faster when there is a bulb burned out
the blinker switch shorted out the brake lights... really really common problem, need to replace the switch
Most common problem -turn signal flasher