Rear left and right turn signal lights not working.

Turn Signal Lamps
The STOP/TURN fuse in the instrument panel (I/P) fuse block supplies battery positive voltage to the body control module (BCM) for the turn signal lamps. When the turn switch is placed in the left or right position, ground is applied to the BCM on the left or right turn signal switch signal circuit. The BCM then applies voltage to the appropriate front and rear supply voltage circuits.
Grounds for the various lamps are as follows:
• G100 supplies the right front lamps
• G101 supplies the left front lamps
• G400 supplies the right rear lamps
• G401 supplies the left rear lamps

Replace the bulb

Has the vehicle been in an accident on the left rear side. First check the bulb to be sure it is not defective, trade it out with the side that works properly to test. If the bulb works well then My thought are you may have a shorted wire. The turn signal flasher works by heat build up within the flasher the heat is caused by the load of the bulbs, the load heats the metal spring causing it to open the circuit then as quickly as it cools down the circuit closes again lighting the bulbs.
There is also a possibility of a defect in the turn signal mechanism on the steering column. The turn signal switch on many models does three different things on many models that use the same bulb element / or bulb for brake and turn on rear of vehicle. It controls the circuit for brake light by sending power both left and right side rear when turn signal is in neutral position then when turn signal is in left turn the switch cancels brake light power to left side rear and supplies flasher power to left side while maintaining brake light supply to the right side rear, and so on opposite when the right turn is chosen on turn signal switch. The turn signal indicators on the dash normally run off the same circuit as front turn signal bulb only which is also controlled by turn signal switch. Front has turn signals but no brake light.
I think there is an additional load on the left side rear turn circuit and it could be either a wire that is shorted or the turn signal switch if the same bulb element is used for both functions.
Often times if trailer lighting is connected the flasher will also blink a little faster because of the extra load of additional bulbs.

it's the grounds if they're both flashing fast it's definitely grounds take a test light and see if its got power goes through the test light grounded to the frame and if the light comes on then it's definitely your grounds

Front right and rear right are on a different circuit than the left front an left rear. Locate the Flasher control module behind dash. With key in RUN position check for pulsing battery voltage on the Green/white wire coming out of the flasher control module electrical connector. If no battery voltage, check for battery voltage coming into the flasher from the turn signal switch on the white/red wire. Left turn input is on the white/black wire. If not battery voltage on white/red, but voltage on white/black when turning left, then the turn signal switch is bad

Bad bulb ,& or socket

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

the next step and almost certainly the problem is the turn signal switch, have seen this symptom on other years around yours and switch fixed it.

It may be a turn hazard module under dash.that is the culprit! The power to the third brake light does not go through the module, but the rear brake lamps power is controlled through this module. I am looking at a drawing of one and it looks like it has two connectors with about five wires in one and six in the other. It has some cooling fins on it also.