I don't think the problem is in the LED's. You've got a bad bulb most likely one of the park lamps on the right side. Seen it before. One of the filaments breaks and touches the other filament in the bulb. It causes a cross feed across the lamps.
Try removing the park lamp bulbs, one at a time and see if the problem goes away.
Other then that, you may have a turn signal switch gone south on you.
97 Sahara, 74 Renegade, 72 CJ5, 55 Willy's (the Beast) Boss 302, 6:34 gearing, Bose 901 speakers.
God I miss that Jeep. Forgot the kinda Jeep, 80 SX4.