It appears to be the signal wiring harness. I can see in the first pic that the bulb is broken, so that is why it is flashing so fast. It must have come loose from the light assembly.
Here are the directions for replacing the bulb. You will need to remove the headlight assembly. I will include those directions, too. It is really an easy one to do. Once the assembly is out, route the wiring the same as the other side and replace the bulb.
The attached pictures correlate with removal and replacement of the headlight assembly. The directions are for headlight bulb replacement, but it shows how to remove the assembly.
1999 Buick Regal V6-3.8L VIN K
Park/Turn Signal Lamp Bulb Replacement
Vehicle Lighting and Horns Turn Signals Turn Signal Lamp Turn Signal Bulb Service and Repair Procedures Repair Instructions Park/Turn Signal Lamp Bulb Replacement
PARK/TURN SIGNAL LAMP BULB REPLACEMENT
1. Remove the appropriate headlamp assembly.
2. Remove the rubber access cover from behind the park/turn signal lamp bulb.
3. Rotate the park/turn signal lamp socket counterclockwise to release.
4. Remove the bulb from the socket.
1. Install the bulb to the park/turn signal lamp socket.
2. Position the socket to the headlamp assembly, then rotate the socket clockwise to secure.
3. Install the rubber access cover to the headlamp assembly.
4. Install the headlamp assembly.
Here are the directions for the headlight assembly. Again, these directions are for headlamp replacement, but it is the only thing I have that shows how to remove the assembly.
1999 Buick Regal V6-3.8L VIN K
Headlamp Assembly or Headlamp Bulb and/or Cornering, Sidemarker, Park, Turn Signal Bulb Replacement
Vehicle Lighting and Horns Headlamp Service and Repair Procedures Headlamp Assembly or Headlamp Bulb and/or Cornering, Sidemarker, Park, Turn Signal Bulb Replacement
HEADLAMP ASSEMBLY OR HEADLAMP BULB AND/OR CORNERING, SIDEMARKER, PARK, TURN SIGNAL BULB REPLACEMENT
1. Raise the hood.
2. Apply light pressure to the headlamp lens to hold the headlamp assembly in place while removing the retainers.
3. Lift up the headlamp assembly retainers to release, then remove the retainers.
4. Carefully remove the headlamp assembly mounting tabs from the slots in the upper fascia support and the fender reinforcement.
5. Disconnect the electrical connector from the headlamp assembly.
6. Remove the headlamp assembly.
1. Connect the electrical connector to the headlamp assembly.
2. Carefully position and install the headlamp assembly mounting tabs to the slots in the upper fascia support and the fender reinforcement.
3. Apply light pressure to the headlamp lens to hold the headlamp assembly in place while installing the retainers.
4. Align the headlamp assembly retainers over the headlamp assembly mounting tabs, then press the retainers down until fully seated.
Check to be sure that the headlamp assembly is securely retained.
5. Close the hood.
6. Check the headlamp aim, If a new headlamp assembly was installed, or if service or repairs in the front end area may have disturbed the headlamp mounting brackets. Refer to Headlamp Aiming.
Let me know if that helps you or if you have other questions.
Images (Click to enlarge)
Friday, August 30th, 2019 AT 9:13 PM