Just taking a quickie peek at the Coupe service manual it looks like it could be several things. Fuse #4 in the Underhood Accessory fuse box controls the blinkers. That's the fuse box located on the drivers side, in the engine area; a longish looking box.
The manual also lists the body control module & the illumination control module as possible issues along with the Multifunction sw. (also known as the turn signal lever).
The illumination control module is located behind the dash on the left side of the steering column, the body control module is stuck in the same box as our ECU; on the passenger side.
I'd try replacing the fuse first. If that doesn't work, pop off the cover to the ECU & gently wiggle the boards inside. Make sure all of the connectors on the boards are seated decently.
Good luck, Nox & keep us posted!