1993 626. Rear left turn signal doesn't illuminate and the front left flashes rapidly.
Also the 4-way flashers don't work on that bulb either. Have replaced
bulb but no change and the replacement bulbs work on other side.
Volt meter shows what appears to be correct voltage (matches
voltage to the right side.) A weird thing was that when I accidentally
shorted the good side with the voltage probe, I noticed a lot of sparking
whereas on the bad side there is no sparking, in spite of there being
voltage there. Does this mean my flasher module is on fritz?
Is that a part only the dealer carries? And how do you physically
remove the flasher module? (I located flasher module under dashboard
near fuse box and can remove the
white 8 wire plug from it, but no clue as to how to remove the module
itself.)

 

that plug in is the flasher. you sould be able to get that at any auto parts store maybe even walmart.

 

Would not think it likely to be a fault with the flasher module bleepbloop. The wire that is Green w/ Black stripe at the flasher module is the output wire for the left side turn/hazard lights for front, rear, and instrument cluster. If module was bad would not expect to seeany of them working. Would more suspect a wiring or connection problem. If you have a 12volt test light then see if it will flash right at the socket with bulb removed. If not or is very dim then move back down the harness a little bit and probe the wire and see if is better. Might just be a bad connection at the bulb socket connector or socket itself. The inside of the socket is not all corroded is it??

 

Today it just started working without anything being done. Based on what babyhuey said about the front and back being on the same circuit, I'm guessing there is an intermittent bad connection to the "bad" light. Next time it fails I'll be more methodical in jiggling lines and stuff to try to narrow down where the problem is. Thanks for that good info.
That is a relief of sorts: the flasher unit for this car is $64 from dealer and $44 from other online sources. Some parts places looked it up and told me it was a $14 flasher but when I saw the part I realized that it wasn't the same electrical/mechanical connector at all.
This spontaneous cure happened a few weeks back when I first started messing with it, changing light bulbs and stuff. At the time I figured it was a light bulb that had a flaky element but there's a new bulb in place now.