97 Kouki.
No running lights in the rear, nor cluster lights.
What would be the first place to start?
BCM possibly?
bcm? these cars dont have bcm’s??!?!
fuses?
i have the same problem in my b16 civic… if u find out dylan send it my way
grounds fuses or relays
tcu?
Had this same problem couple years ago… (on 95 zenki) likely a ground fault, just check the fuse, if you put another one in and it goes as soon as you turn on lights theres your problem… GL finding that though… for me I think it was my licence plate light as i never found the fault and ended up rewiring the taillights and corners with new wire from the fusebox (didn’t realize that that light was on the circuit too)… also check for any blown bulbs in tails or corners there could be a short… Definitely one of the most annoying problems I’ve ever encountered 
I cant remember for sure but i think the cluster lights are on that same circuit, could be that dimmer switch too :S just try to remember the last things you did to the car and where you could have come close to that line and possibly created a short. Look at the FSM to find where the circuit goes and if it comes to it, just trace it. (actually the FSM is probably your best choice after checking the bulbs and likely places)