2004 LeSaber. Left (only) turn signal does not work.

If the right side works it's not your flasher, Its your left side bulb, either front turn signal or rear tail light bulb.

The wiring for your left turn/hazard might be damaged. The turn and hazard signals use the same bulbs and wiring, but get their signal from different switches.

either wrong signal bulb or short in left turn signal wiring if both left signal lamps not working.if only one of left turn signal dont work could have corroded bulb socket spray a little electronic cleaner in bulb sockets see if left signal work.

You say it's the right turn signal that is malfunctioning. If the left works correctly, then the problem is most likely NOT the flasher unit. That unit provides the flash for both left and right signals. I think that flasher unit is mounted on your steering column, down under the dash. It will probably be an aluminum cylinder, but may be a rectangular black plastic block. Before you change the flasher unit, I'd suggest checking the front and rear turn signal light bulbs. On the front, those are the parking light bulbs, and on the rear are the stop light bulbs. You may have a poor connection, probably from corrosion, or the bulb is very nearly burned out completely. Good luck.

Check the bulb socket for a burnt or a shorted condition. Remove bulb and try another bulb, if it does it again then you have a short in the socket or wiring to bulb. Turn on the 4 way flashers and see what it will do. If it continues then look for any burnt wire connector or wireing to bulb. Check the wiring behind the light for any metal that has cut into the wiring insulation. Hope this will help you.

You have a bad ground wire on the right rear.
if you need further info let me know.

loose wiring or bad fuse

check the front right bulb

Well, seeing that you have a multimeter, check power at the socket and make sure it has power there. If there isn't then your wiring has an issue somewhere.

sounds like the bulb you have is the wrong resistance the new noen bulbs will do this