Left blinker light stays on solid when headlights are on

Could be the turn singal relay not getting the correct power when lights engaged. Take out bulb from headlight and then turn on headlights. Now no power to the headlights. Try to turn on blinkers now. If they blink replace signal relay, if they still are solid it may be your flasher. Just a guess without looking. Thanks.

You may need to replace the blinker controller, a small device that manages the timing and sequential on/off to the bulbs.

Your right rear turn signal bulb is blown.Replace the bulb and the fast blinking will stop.

mporteous, It sounds like you have a light switch problem. I can't think of any other reason for the running lights and tail lights not working in this situation. Are your brake lights working when the headlights are off and how about when they are on? Do your four ways hazard lights work in these situations? Try all the lights under these conditions. The reason the left turn signal blinks very fast is because one of the bulbs are burned out. Try the left signal and one light (front or back) will stay on and the other will not come on at all. Replace the bulb that does nothing. Do this before you try all the lights in different situations. I think that you will have to replace the light switch. Good luck with this.

start by looking for a bad ground to one of the light sockets

It sure sounds like you have a case of "sneak circuits"
These are usually caused by a bad ground somewhere and something is "grounding" through the light bulbs.
Have you changed any wiring or installed a stereo or some other accessory?
You might use a jumper wire and ground the dash and other areas to the negative battery post as a way to find the culprit.

no year compass stated, so will do 1st year.
USA/ Car?? (we are USA forum so answers default to bingo us)
engine runs ok, all else runs OK> just lamps problems?
Just is very important word in the electric world.
Drivers ok? too. (engine cranks, runs and stays running?) (turns on many meal all that)
gen1 is 2006 to 2016, later is GEN2.
ill pick first years.
seems headlights/binkers (turns sigs) are shorted together or parks.
Park/(aka, tails) may be in the mix.

1: fuses check ok
2: battery fully charged, reads 12.6v key off rested, and 13.3 to 15vdc running,
3: check for wiring damage behind lamps on the effected sides.
and for trailer hitch from H3LL hacks. there? looking is first.
collision damage by other owners, is possible (if 2nd owner you)
now electrics have a chance to perform. good power.
This system is all networked now.. needs to be understood
the first step now is to SCAN it. that's right, what if the communications bus, cant all talking between modules.
those lamps are all run by a computer under the hood
called TIPM , the module insides is called the "electronics module. EM"
it has 4 blinker wires as an output. (not shared a key fact for diagnoses)

you said driver side blinker (left works better)
drivers in UK are on right.
the left side front and rear. my guess , NO not rear)
if true the problem is there, left front blinker.
wire damage there, even the LAMP it self can short, (get new one?)
blinker,
damage at TIPM , can be possible look there yet.
its just a computer and has transistor drivers. to lamps
and if it told to do something, and is told correctly(scans)
then its bad or its output wires are shorted.
try a new lamp ?

Refr. page 50 in the SM ( MK jeep service manual, SM)
and 52.(turns)

the 4 head lamp wires(power) all are seperate at the EM
not parallel at all. independent, x4
and last the park lamps are independant on the EM
that means if the lamps are good and wires good then the EM
is faulting.
or its getting wrong commands, on the CAN-BUSS network
now you know how it works,
better is get the SM and read, it covers ALL this, in vivid details.

THERE IS A BLINKER RELAY UNDER THE DASH. IF YOU CAN GET ONE OF THE BLINKERS TO BLINK YOU CAN HEAR THE RELAY LISTEN CLOSLEY THEY PUT THESE THINGS IN SOME HARD TO GET PLACES

check the relay and blown out bulbs will cause the lights to blink fast or some to stay on. one bad bulb will cause the problems.

That's an issue with wiring somewhere alont the line. There has to be a short somewhere. Hopefully for you the short is from the new taillight assembly being installed and it would be relatively easy to get to. Hope it helps!