Many drivers rely on turn signals or hazard lights to inform them of when to slow down or change lanes in every vehicle --- including the 1999 Grand Cherokee. Failure of either of these lights poses a safety hazard.
The flasher unit is a canister-shaped relay. The flasher unit turns on the signals and hazard warning lights when you activate the switch.
You should hear an audible click when the flasher unit is working correctly. If the turn signal fails on one side and you do not hear a click, the turn signal bulb is likely faulty.
Look in the fuse panel of your 1999 Grand Cherokee for a blown fuse. If the fuse has not blown, replace the flasher unit, located in the fuse relay box to the left of the steering column.
Detach the malfunctioning flasher from the fuse panel. Attach the new flasher unit.