Jan. 28th 2011, I had an appointment to get my 1994 (XJ) inspected. On my way to work in the morning, my right headlight blew, so after work I replaced it before the inspection.
Everything passed, paid the $55.00 bill, and left. 1 hour later making a right turn, my indicator light on the dash came on and stayed on (even with the switch off), and the marker lights front & rear (right side) weren't on. The left side works like normal. Headlights & Hazard lights, reverse lights, brake lights work like normal.
I replaced the Flashers & changed the fuse, still the same.
Cleaned the plug below the airbox.
When I pull the switch **** out the right indicator light comes on, on the dash (without the key in), and the lights come on (including right side), but when I put the key in and turn to accessory, the right markers are out (indicator still lit on dash), but when I put the right signal on it works, shut it off, and the lights go out.
Does anyone have any clues or suggestions ?

Here is a picture of indicator light on dash with **** pulled out (no key in)

 

No one has any clues of what to check next ?

 

Does the indicator light stay solid or does it blink? I've never seen that before but maybe it's a grounded wire somewhere

 

I have the same issue. But my right blinker will not blink nor even come on when I turn the lights on. BUT the light will come on with the hazards.

 

Your right parking light is back-feeding through your right signal light. You have double filament bulbs in front and rear. Two separate filaments in each bulb. One is signal and one is parking with two contacts. Either a # 1157 bayonet type (push and turn) or a 3157 newer style push in. The problem is You are either using a single filament bulb by mistake somewhere on the right side, or the two filaments are touching in one of the bulbs, or you have a bad ground or contact between the bulb and socket. Should be pretty simple to fix. I hope I've made myself clear. If not ask.

 

Well after a couple of days of switch, bulb changing, I decided to start tracing wires. Since my right headlight blew last Friday, I started there.
Headlight, and side marker grounds were good. I cut open the rubber boot on the marker below the headlight, and sure enough the ground was broken. Not to get my hopes up, I connected a piece of wire from the ground to the base of the socket and tried the lights and
" WALA " I found the problem. Everything is back to normal.
All lights work like they are suppose to, and the indicator light on dash is out.
So if anyone is having turn signal issues, check your grounds on the marker lights, even if you have to cut open the rubber boot, it will save you a bunch of money buying new parts, that you don't need.
Pic's included
Mac

 

There you go bad ground. Thats a signal /parking light not a marker.