There is a signal flasher that controls them, maybe be even two. One for the directionals and one for the hazzards. There are small plastic devices that plug into the wire harness under the dash. They can be hard to locate unless you know what you are looking for.
I see if I can link to a image of one...
Do the hazzard flahers work? If so they it the turn signal flasher
Here is the GM part number, both the hazzard and turn signal use same part but I can't tell if they are one for each. AC Delco does not provide an image of one.
1998 CHEVROLET LUMINA V6 3.1L 189cid GAS FI N Engine VIN = M
ELECTRICAL / FLASHER-TURN SIGNAL QTY=01 12450013FLASHER,HAZARD LP & T/SIG LP