Try removing the turn signal diode. See photo 47 on page 12-7 of ETM, It is under the seat.
This diode pack is for the flashers, if one of the diodes is shorted, it would cause this symptom. Nearly all the current meant for the turn signals would travel through the shorted diode instead. Removing the diode will only disable the flashers, so you won't hurt anything if you pull it out and try the signals. If they work when you remove it, you have found the problem.
If the diode is good, then you probably have a short to ground somewhere in the left turn signal circuit, shunting the current to ground.