I have a 2001 CBR600F4i. Both front turn signals stay on the whole time when not blinking.

Right rear turn signal also stays on the whole time when not blinking. Left rear turn signal is always off when not blinking though. But everything blinks though when needed.

In the instrument cluster, the right signal indicator is always on also. However both the indicator blink as they are supposed to when I use them.

I tried different lightbulbs, they are not the issue. The rears have been replaced w/ LEDs by previous owner.

Anybody got any idea why its acting like that?

 

I'd guess that the running lights were wired into the blinkers and a diode was not used to keep the signal from feeding back into the system and creating a loop. You are going to have to trace all the connections in the rear lights and figure out what is going on. It sounds like the fronts are working fine, with the running lights on all the time and the indicators flashing. You can download the F4i manual off the interwebs which contains the wiring diagram.