Download the 2005 KJ Service Manual here...includes circuit diagrams.
I am assuming that you have an Export model seeing as you call it a "Cherokee"....some slight changes in the wiring diagrams! If a USA model then check fuse 7 and 9 in the Junction Block...(internal fuse panel) and swap out relay "Park Relay"...top center small relay amongst group of 9 relays on rear of Junction Block.
You will see that the multi function switch tells the the Hazard Switch that the indicator lights must either flash on the left or on the right or do nothing at all. So effectively all the indicator/marker Lights on the LHS are in parallel and the same with the RHS...if any one of these bulbs is blown then the Hazard switch picks up the lower current draw and flashes faster to alert you to the fact that one of the bulbs is not flashing.
The fact that all the lamps flash when you switch on the hazards shows that the basic lamps are OK as is the wiring to them.
If you are saying that the complete LH side does not work...other than with the Hazard Switch...then definitely the Multi function Switch is faulty or the wiring going from it to the Hazard switch is faulty.
You will see on page 8W-52-2 of the wiring diagram that a Light Blue/White wire goes from the multi function switch Pin 10 and goes to the Hazard switch pin 9. When you move the multi function switch to the right to make a right turn you switch ground along this line from ground point G202.
The left side works the same, ground is switched to the Hazard Switch pin 5 using a White/Light Blue wire from the multi function switch pin 6. So if this is the case that the LH side indicators are not working, leave the multi function switch indicator stalk in its central position and ground the White/Light Blue wire... ie. a White wire with a Light Blue stripe...to a clean chassis point somewhere. The left flashers should work.
The best way to do this is to carefully piece the wire with a pin or needle so that it pieces the insulation and goes through the copper wire inside...do this near to to the Hazard switch side....now touch this pin with a short section of lead onto a clean chassis point.
If this works then you either have a break in this wire somewhere or the multi function switch is faulty.
If you are saying that only the Left Rear indicator does not flash when turning...and the Front Left does flash OK...then it has to be a grounding fault at the left rear socket or the Tow Package has to be removed completely.
Here are the Manual:
http://www.colorado4wheel.com/manuals/Jeep/KJ