1997 Hyundai Accent is acting funny in the headlight department. At first my day-time running lights didn't work and low, high, and flashers were fine. Now, day-time running lights work, high beams work, and flashers work, but the low beams alternate every day or so between working, left side not working, and right side not working. I've checked the fuses, checked the bulbs, and checked the sockets for the bulbs. All are fine. What could be causing this? (Have yet to check relays.)

Your fogs only working when low beams are on is normal, as far as your low beam lights not working, I would have the headlight switch checked, or check for a bad fuse or possibly a relay if your car has a light relay. Some do and some don't, I am not that familiar with your model of car to tell you for sure.

Check the bulbs could be blown low beam

Did both lights go out at the same time? And do you have blinkers, and flashers?

Get a schematic and trace out the power source to those devices not working.

check the fuses first, no luck replace the day time running light module.

Check for headlight relay and fuse. Some cars have separate circuits for head light flasher and normal high/low beam. From your description, I would suspect a bad connection to/from relay or relay itself.

Under the dash fuse box ,fuse 15 (TCM ECT) is a combination of cluster, heater and headlights.probably a relay fuse!!!!! fuse 16is a relay fuse.

possibly head lamp switch. daytime running lights on separate circuit and use the high beams at reduced voltage. does flash to pass work? that's high beams too. do high beams work?

Is it just low beams?
do taillights work?

ya know it kinda sounds like the headlight switch that switches from high beam to low beam has a bad contact. You don't have one of those 4-beam modules that turn on all 4 lights on high beam do you? that thing screwed my whole headlight system up, I ended up throwing it in the trash.

I have the chiltons and haynes manual, I'm sure between the two we'll find a good diagram. I gotta get my youngin to open house at school, but I'll pull the books out and send you the wiring diagram.

Lihgting switch must also be checked