electric problem

Try replacing the (how do I say this without sounding like a peeved British) "blinking unit" or (*crude American) "flasher unit"

What I'm trying to say, is that since your problem is directly linked to working only when the lights flash or blink on and off, check the small module that controls this. There is a bi-metallic strip inside that breaks the contact when current flowing through heats it. Perhaps the contacts are stuck in the wrong posiition so that your lights only work when the blinkers are in use.