Where is the location for the flasher for turn signals on a 2008 Kia Optima?

The side that is dim has resistance in the electrical circuit , use voltage drop testing to find the problem . Watch this video on voltage drop testing .

https://www.youtube.com/watch?v=YaYtCVBodpw&t=1s

fast blinking is a sign that the flasher relay has a fault , change that and i would expect the fog light issue will resolve as well , as i expect the flasher relay is trying to earth through a different circuit

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.

hope this helps!

The speed sensor is located on the top of transaxle asm,

It's likley that the left rear signal bulb has burned out and needs to be replaced.

Check the flasher for the turn signals

Normally when this happens you have a blown bulb on either the front or rear the fast blink is because with only one bulb working the flasher clicks it faster less of a load means faster blink.

You have a bulb out somewhere could be front or back, but that is usually why it blinks faster.