Turn signal lamp will not blink when system is armed

Make sure that all the bulbs are the correct ones and have a good ground.

The turn signals are controlled by the BCM
Turn Signal Lamps
The body control module (BCM) is responsible for controlling the turn signals and hazard lamps. When the turn signal switch is placed in either the left turn or right turn position, the BCM receives a signal from the turn signal switch. The BCM 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 pressed, the BCM receives a signal from the hazard switch. The BCM then will send an on-off voltage signal to all the turn signal lamps. All the turn signal lamps will flash including both IPC turn signal indicators.

I would suspect a problem with the BCM or maybe corrosion in the under hood fuse box . Wires from the BCM to the front turn signals go through the underhood fuse box.
Your best bet ,take it to a qualified repair shop that has a diagnostic scan tool that can read BCM DTC'S - diagnostic trouble codes
DTC B3948 Left Front Turn Signal Circuit
The body control module (BCM) controls the left front turn signal, hazard lamp, and daytime running lamp (DRL). The BCM supplies voltage to control the lighting functions. The BCM monitors the left turn signal lamp supply voltage circuit for proper operation.
DTC B3949 Right Front Turn Signal Circuit

* Make, Model, Year for specific information.
* Check warranty. call for service.
*** Following is for information only. ***
* Older (Non-Computer) cars blinkers will blink faster if one of the lights are out (front and back turn signals)
* Some of the Luxury models have side blinkers and mirror lights. These will also affect the blink rate.
* Newer cars usually have a digital warning if a lamp is out; "Left Signal Error", etc.
* Turn on your lights and signal lights and have someone look around. Note; some cars won't blink or turn on unless the motor is running or the switch is in "running" mode. "AC" position does not always work. Check for lamps that are not working.
* Note that the newer cars must use exact lamp replacement or the lamp may crash the computer system. Use MFR approved parts.
* Exact replacement of older bulbs are required as they affect the speed of the blink rate. Check if the blinker bulbs were replaced with MFR approved parts.
* Check if the right type of bulb was installed. Some have double filaments for Brake and running. Blinkers are normally only one filament. But it's possible to have a double or triple lamp in really older non-standard models.
* Final, Check your battery for corroded terminals or a dead battery. Check the 2nd wire on the RED (+) lead for a good clean connection. This is the wire that goes to all the electrical system of the car. Clean and reconnect.
* Check with your dealer for further information.
Aloha, ukeboy57

What fuse are you pulling ?

Hazard Lamps
The hazard warning switch is part of the turn signal switch. The turn signal switch receives battery voltage at all times through the HAZARD SWITCH Fuse. When the hazard switch is placed in the HAZARD position, battery voltage is applied to the hazard lamp/turn signal lamp flasher. The hazard lamp/turn signal lamp flasher sends a turn signal flasher signal to the turn signal switch. The turn signal switch provides all of the turn lamps and turn indicators with the turn signal flasher signal, simultaneously flashing them on and off.

Turn Signal Lamps
The front turn signal lamps are made up of the front park/turn signal lamps and rear turn signal lamps. The front turn signal lamps flash with the rear turn signal lamps when a turn is initiated using the turn signal/multifunction lever. The turn signals will operate only with the ignition switch in the RUN position and will not operate during hazard flasher operation.
When the ignition is turned to the RUN position, battery voltage is supplied to the TURN SIGNAL Fuse. Battery voltage is then applied through the turn signal fuse circuit to the turn signal switch. When the turn signal switch is placed in the LH or RH position, voltage is supplied to the hazard lamp/turn signal lamp flasher. The hazard lamp/turn signal lamp flasher supplies a turn signal flasher signal to the turn signal switch. With the turn signal switch in the LH or RH position the corresponding turn signal indicator, rear turn signal, and front turn signal receive the turn signal switch signal and will flash. The front turn signals receive the turn signal switch signal from the turn signal switch via the BCM. The turn lamps are permanently grounded.

Replace the turn signal switch. Refer to Multifunction, Turn Signal, and Hazard Switch Replacement - On Vehicle in Steering Wheel and Column - Tilt.

Hi there., when flashers/indicators work rapidly on the dashboard you should check whether it is the same on the actual bulds. Fadt flashing is usually a sign of a bulb failure somewhere. If everything is functioning ok externally I would consult a competent technician for a diagnosis.

Here is what the service manual says. Looks like it is not a flasher relay but a function of the body control module.

TURN SIGNAL AND HAZARD WARNING LAMP SYSTEMSystem Description OUTLINE Turn signal lamp and the hazard warning lamp is controlled by combination switch reading function and the flasher control function of BCM.
TURN SIGNAL LAMP OPERATION - BCM detects the combination switch condition by the combination switch reading function. - BCM supplies voltage to the right (left) turn signal lamp circuit when the ignition switch is turned ON and the turn signal switch is in the right (left) position. BCM blinks the turn signal lamp.
HAZARD WARNING LAMP OPERATION BCM supplies voltage to both turn signal lamp circuit when the hazard switch is turned ON. BCM blinks the hazard warning lamp.
TURN SIGNAL INDICATOR LAMP AND TURN SIGNAL SOUND OPERATION - BCM transmits the turn indicator signal to the combination meter with CAN communication while the turn signal lamp and the hazard warning lamp are operating. - Combination meter outputs the turn signal sound with the integrated buzzer while blinking the turn signal indicator lamp according to the turn indicator signal.
HIGH FLASHER OPERATION (FAIL-SAFE) - BCM detects the turn signal lamp circuit status by the terminal current value. - BCM increases the turn signal lamp blinking speed if the bulb or harness open is detected with the turn signal lamp operating. NOTE: The blinking speed is normal while operating the hazard warning lamp.

check socket ground

I would suspect the brake light switch, located above the brake pedal and attached the pivot
on the brake pedal arm. If that is not the problem, it could be in the turn switch. When the turn signal is on ,the turn switch turns off the brake lamp that direction, so the lamp will blink in that direction. Try to wiggle the turn signal lever with brakes on and see if they try to work

Please check the cables lead to your rear turn lamp for loose connection. Both turning lamps ( rear and front) should work to keep turning lights back to normal blink.
Regards

Replace the bulb that stays on and doesn't blink, if that doesn't solve the problem, let me know.