My driver side turn signal only works during the day

Your hearing it coming from the diver side front speaker . There is no relay , the BCM - body control module makes the turn signals work . What problem are you having ?

Turn Signal Lamps
The FRT TRN/HAZ/CRTSY/MIRR/CARGO and REAR TURN/HAZ fuses in the underhood fuse block supplies battery positive voltage to the body control module (BCM). When the turn signal switch is placed in either the left or right position, a signal is sent to the BCM to illuminate the desired turn signal lamps. The BCM has an internal flasher that sends an ON-OFF voltage signal to either the left or right turn signals and their instrument panel cluster (IPC) indicator. When the hazard switch is pressed, a separate ground signal is sent to the BCM to activate and flash all turn signal lamps including both IPC turn indicators. The front and rear turn signals are grounded at G105.
The IPC illuminates the TURN SIGNAL ON indicator in the driver information center (DIC) when the IPC determines that the turn signal is active for more than 1.2 km (0.75 mi). The BCM sends a class 2 message to the radio in order to activate the audible warning.

Your best bet , take it to a qualified repair shop.

you have obvious short in the wiring - check the bulbs first, then the wiring. it is rarity to exchange relay - if it was not physically damaged during accident.

Sounds like its a bad bulb or the grounding on it. I had the same problem on my 06 Colorado. I bought new bulbs put on in and it still didn't work turned around and put other one in and it worked. So I'd try that first

This behavior is usually caused by water leaking into the socket or just a bad socket. Clean it up and use some dialetric grease on the contacts.

Do you know anything about automotive electronic's ? body control modules , ford's SJB - smart junction box. Do you own a professional scan tool that can read codes in the SJB ? Auto part stores can not read these code's . Do you know how to do automotive electrical trouble shooting ,using a DVOM -digital volt ohm meter ? If not , your best bet would be to take your vehicle to a qualified repair shop.
Principles of Operation
The smart junction box (SJB) sends multiple voltage reference signals to the multifunction switch. When the multifunction switch is in the LH or RH TURN positions, or the hazard lamp switch is engaged, that input signal is routed to ground.
When the SJB receives a request for a turn signal or hazard lamps, the SJB supplies voltage to the appropriate turn lamps.
Do you know what a wiring diagram is ? Free one's here
http://www.bbbind.com/free_tsb.html Enter vehicle info. year , make , model an engine size . Under system click on lighting ,then under subsystem click on turn signal lamp . Click the search button then the blue link .

About your 1992 Buick Park Avenue 3.8L SFI OHV 6cyl. the Flasher is located:
Hazard flasher: Front seating area, driver side, under dash, mounted above kick panel

Turn signal: Front seating area, driver side, under dash, driver side of steering column, mounted on support bracket

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make sure our lights at rear are grounded sounds like a bad earth

Sounds like you need to replace the drivers brake/tail light.

This simply means that the front driver side turn signal bulb has failed. Replace it.

INTERIOR FUSE PANEL IS LOCATED UNDER THE LEFT SIDE DRIVER SIDE.OF THE INSTRUMENT PANEL.BEHIND THE FUSE PANEL COVER.CHECK FUSES.IF THEY ARE GOOD PROBLEM IS IN THE COMBINATION SWITCH.