97 cherokee here are my symptoms
With key on lights off-
Left signal on it works fine
Right signal on it blinks but the odometer and 4wd floor light blink with the signal but opposite each flash also the headlights blink too.

With key on lights on-
Left signal works but it blinks both front blinkers
Right signal stays solid on dash and lights up all brake lights and both turn signals solid.

I have no idea what is going on.....ive checked all fuses and bulbs are good. Blinker switch and headlight switch are new. Looked at the wiring for lights and i dont see any broken wires. Any help would be great!!!!

 

Did you just get this jeep? Because i would say the turn signal controls are wired wrong.

 

Sounds like a grounding issue to me.

 

no i have had my jeep for a few years now. the only thing that i can think of that isnt stock is my led tail light boxes. i checked all the wiring and nothing is broken. i have had these lights in my jeep for about a year now and this issue just occured yesterday..

 

oops i missed the part where the switches are new. Did this start happening after the blinker switch was replaced? Otherwise i would agree with Belvedere.

 

no the switch for blinker and headlight were replaced last year