On my 2004 Hyundai Tiburon, My dash and running lights (parking and tail lights) dont turn off, I've been disconnecting my battery, I removed the body control module (BCM), one of the relays clicks every time i connect the battery, could it be a defective relay or another component in the circuitry? or not the BCM at all?

First thing I would check is all frame grounds... like the negative battery cable and the grounding strap on the passenger side motor Mount to the wheel hub. In any electrical system, lights draw more current than anything (except the battery) when you turn them on... Check the grounds!

I've got a 2003 Suburban that has two fuse panels, one inside under the steering wheel and another under the hood, drivers side behind main battery. All lighting fuses are under the hood, Plastic cover with battery symbol pulls up to remove, should be a panel schedule inside the cover. The tail light fuses are in upper left section labeled RR Park and LR Park.

Under the vehicle by the tail lights locate the lights wiring and look for this colors.
it's only four colors white-ground point,brown-parking lights,yellow-left side turn signal light and green-right side turn signal.
you are going to need a test light to find the correct wire,if you can't locate the wiring unther the vehicle then remove the tail lights and do the connections there.

More than likely that is your problem. It should be up under the dash on the drivers side somewhere but i could be wrong. here is a crappy pic of it.

When you turn the key, do you hear a click from under the hood? If so, then maybe your battery is dead.

did you check if power was reaching the socket? you will need a test light to check, I would by one, it will come in handy for years. see if power is at the socket, if so there is a bad ground, you need to verify that to not waste a lot of time guessing, if the turn signals work OK the ground is probably good and there well may be a problem but check power in the socket first.

Open your hatch and behind the tail lights you will see panels with plastic knobs you can unscrew. Behind there are 3 8mm nuts you need to unscrew which will let you remove the whole tail light assembly. There is a post on the actual tail light assembly that holds it in so you may have to give it a firm pull to actually seperate it from the car. If you have the stock infinity sub you will need to remove that first to get to the drivers side tail lamp.

i had the same problem, well my right turb signal stayed on all the time and i had to pull the fuse. the BCM under your dash is bad. the BCM is where all your fuses are plugged into. you can find one online for about $700ish. go to hyundaihouseofpower.com or newtiburon.com and they might help you. 03 tiburons have bad luck when it comes to the BCM. change it out and your problems will be solved.also look on ebay.

marker lights?? queens english please .Do you mean the side lights or evan running lights please be more explicit