Blinkers come on steady rather than flashing. The flasher relay seemed as though it wasn't breaking the current flow to the blinkers, with a constant whine coming from the relay when the blinkers were engaged. Replaced the relay, and the new relay has the same constant whining noise, and the lights still remain constant rather than flashing. I'm not sure if it is a K1, 2, or 3. It's a '79.

The blinkers work through a flasher relay. This might have failed. Try turning on the hazard flashers to see if they blink. If they don't flash it is probably the relay at fault. Please note some Buick models use separate relays for the blinkers and the hazard lights. If the hazards work and the blinkers don't you've got a 2 relay version. Sparky Answers Changing The Flasher On 2003 Buick Century

Both blinkers come on at same time ? on steady or flashing ?

possible faulty flasher or relay, check all signal light bulbs and wires for damaged or burnt sockets, do you have trailer hitch wiring, if you do look for damaged wires etc., It sounds like a grounding issue.

dont break the brakes..... TURNS & HAZ
many blinker, modules , internally flash with any load.
1: check all fuses first... (SOP)
2: then remove the blinker loads from the timer.

see it here
http://www.jeep4x4center.com/knowledge-base/index.htm?utm_source=cj#service

see WIRING, (end)
8w-51/52
chapter 8w, page 51-4 shows the switch. (complex it is)
note how brake and turns are shared, resources. (blub elements)
now 8w-52-6
see the flasher module.
see C305 pin 2, any load on that pin will cause it to flash.(inside)
that would be any switch in the combo switch stuck on.

There is more than one flasher. One is for hazards and the other flasher is for directional signals. They are located under dash just left and right of the steering column. Don't go tearing up the steering column, then you are asking for trouble. Try the least expensive and labor intensive fix first.

You have some burned out filaments. On dual filament bulbs the "blinkers" I am taking it to mean the turn signals. They are one filament. The "Flashing Caution lights, work on a relay circuit, which sends a larger amp current into the opposite filament then the turn signal. Check front & rear bulbs.

I used to have a 76 XS500. Got lots of compliments with that bike.
The wattage of the bulbs is important on how the blinkers work. The rate they flash, and if they flash is dependant on the current being drawn from the lights. Thats why many times if you have one light out the remaining light may stay on solid or flash faster.
You could try removing one bulb on each side and see if the blinkers work. Then reinsert and remove the other remaining bulbs. If they work normally with one bulb in each side whether front or rear then I would suspect the flasher relay.
Say the fronts work when the rear are out and the rear don't work when the fronts are out then I would suspect either the bulbs or sockets or your solder connection or switch.

You may also look into an electronic flasher. They automaticaly adjust for variable loads to flash so they flash at a normal rate.

That's normally a good sign.

I'd just check them out, switch on the 4 way flasher/emergency lights and walk round the car. If they're flashing on all 4 quarters. Its OK.

the flasher and the blinkers are serpent elements of the bulb and also have serpent flashers if none of your blinkers flash when manually doing it chock flasher it is round and usually by the fuss box some times on top there is also one 4 the hazard lights be sure key is on

flasher located at bottom of fuse box its round bout the size of a pop bottle lid,hazard flasher located at top