Left rear turn signal, rear hazard lights not working

Any ideas on what else to check?
Yeah, hook up a professional grade scan tool an check for DTC'S -diagnostic trouble codes in the BCM - body control module. Seeing how it controls (turns on) these lights. Turn/hazard indicators flashing fast means a bad bulb or short circuit somewhere.

DTC B3949: Right Front Turn Signal Circuit
Circuit/System Description
Ground is applied at all times at G200 to the turn signal/multifunction switch. The turn signal lamps may only be activated with the ignition switch in the ON or START position. When the turn signal/multifunction switch is placed in either the TURN RIGHT or TURN LEFT position, ground is applied to the body control module (BCM) through either the right turn or left turn signal switch signal circuit. The BCM then applies a pulsating voltage to the front and rear turn signal lamps through their respective control circuits. When a turn signal request is received by the BCM, a serial data message is sent to the instrument panel cluster (IPC) requesting the respective turn signal indicator be pulsed ON and OFF.

DTC B3951: Right Rear Turn Signal Circuit
DTC B3951 will set when the BCM detects a short to ground or an open/high resistance in the RR turn signal control circuit.

DTC B3950: Left Rear Turn Signal Circuit

DTC B3948: Left Front Turn Signal Circuit

DTC B3445: Stop Lamp Circuit

Get the left signal to flash fast then walk around the car to see which light isn't flashing then change the bulb or socket if they all appear to be flashing (front and rear) turn on the right turn signal then look into the front and rear lens and count the number of bulbs flashing, now do the same thing on the left. Many times there's more than 1 bulb in each lamp. I hope this helps. Take care.

Do you have a burned out bulb, that will affect the speed of the flash

Do you know how to do automotive electrical testing ? Do you know what a relay is and how it works ? Turn signals flashing fast , could be aburnt bulb , flasher module .
VEHICLE RELAYS Operation Diagnosis
Turn Signal Lamps
The HAZ LP fuse in the underhood fuse block supplies battery positive voltage to the multifunction hazard switch assembly. The TURN fuse in the IP fuse block supplies Ignition positive voltage to the multifunction turn signal switch assembly. With the ignition switch in the RUN or START position, ignition positive voltage is connected through the multifunction turn signal and hazard switch assembly to the flasher module which is grounded at G205. When the turn signal switch is placed in either the left or right position, the circuit is complete from the flasher module to the turn signal lamps and to ground. The flasher module then sends an on-off voltage signal to either the left or right turn signals and their instrument panel cluster (IPC) indicator. When the hazard switch is activated, all turn signal lamps will flash including both IPC turn indicators. The front turn signals are grounded at G111 and G112. The rear turn signals are grounded at G475 and G422 on the pickup and G450 on the utility.

Generally speaking, symptoms of a bad or failing turn signal bulb are usually the culprit...in your case, either it's the front left or rear bulb. Varies for different vehicle makes...common signs include:

1. turn signal light staying on solid
2. or blinking very fast
3. or either sides of the bulbs stop blinking altogether.

To test this, make sure you reconnect everything you disconnected.
Turn the left signal light on; go to the front of the vehicle, is the turn signal bulb illuminated? If it lights up, even though it is not blinking obviously the bulb is okay. If it doesn't, replace it- problem solved. You'll do the same procedure for the rear turn signal Is that lit up? If not replace the bulb and the problem is solved.
Another common failure is when the turn signal blinks really fast, same procedure as mentioned above.
If both bulbs for the left side and right side illuminate but don't blink, the problem is in the steering column turn signal switch.
If the left or right side blinkers don't work properly at all...then check the integrated hazard warning/turn signal flasher relay- that may be defective; again, that's usually the case if both sides of the signal light don't work.
If you are blowing any fuses related to the flasher system, you have an electrical overload in the turn signal circuitry.

The wire feeding the front left turn signal is likely crimped or stretched and touching the body somewhere. Do you best to trace the left front turnsignal wire back as far as you can - even just jiggling it might give you short term solution (although it will probably come back).
The fast flash of the rear light is because the short up front is letting too much electricity run through the flasher module. This makes it run too fast. Find the short up front, and both problems will be solved.

In my case the left front turn indicator lamp worked, but not the left rear indicator, although all the lamps would turn on with running lights activated, as well as the backup light and 'night-light' mode. The left rear turn indicator would not work with the hazard lights activated. I tested the combination switch (this is the left/right turn indicator switch you use when driving to indicate which direction you are going and is mounted/located on the steering column) and it tested O.K.. I had good continuity from the combination switch black wire, and resistance on the blue-white wire from there to the left rear turn indicator lamp, as well as good continuity on all wires going out from the left parking light fuse. Since the Haynes manual indicated that the flasher module was probably good if it made the tell-tale clicking sound, I was feeling perplexed. So I took it into a local shop that specialized in auto electrics and it turned out to be the flasher module. I was under the impression that it operated in a straight-forward left-right manner, but apparently it has a different circuit for each turn indicator lamp. So even if it is making the appropriate clicking sound when the combo switch is flipped, it could still be the flasher module. Obviously the manual leaves a bit to be desired in the troubleshooting of malfunctioning turn indicators.

as for the faster flashing thats as simple as a blown bulb, replace the bulb and see if that fixes the problem, it may fix the lot because the other symptoms you mention are a bad connection, if bulb is fine check the connection isnt loose or corroded over. if it is simply file it back to establish better connectivity,

The rear left turn signal bulb must be replaced immediatly before it melts the light socket, if it has'nt yet. Also please verify that the correct light bulb is being installed. because even though many bulbs look the same they are not identical. Installing the wrong bulb can be the begining of many, many problems in the particular circuit

replace the rear bulb it flashs fast to let you know the bulb is bad, whatever bulb is not flashing thats the bad bulb, should be a 1157 bulb or a 1156 if it has one contact it's a 1156 if two it's a 1157