Turn signals light but do not blink

Having the headlights on or off do not affect the issue which is:
When pressing up or down on turn signal stalk to signal your turn the correct light comes on and stays on but does not blink. So I have to manual keep pressing up or down to mimic a turn signal. This happens to both the front and rear lights.
When pressing on the hazard warning button the lights of the front and rear turn on but do not blink either.
All other light functions work fine.
Is there a switch or relay that is supposed to activate the blinking?

Update: now the left turn signal light has been on all night and the battery is dead this morning but the car starts right away after getting a jump, light is still on.