I have not seen the electrical schematic for this car but typically the brown wire in the GM cars is the park lamps wire which probably lights these lamps as well. 

That car may have been serviced or wrecked and had some work done. Get under the fenders and look up in there to see if the wires actually go to the side markers on the car. 

Check for power with a test light. Make sure you have one to verify power on wires and connectors. 

Those may be LED or  conventional bulbs. If you remove the lamps and they are bulbs or LED bulbs in a conventional socket, look in the sockets for crud, corrosion and/or dirt. Make sure the power is off and use a small sharp object to clean the terminals in the socket. Be careful not to cut yourself or damage the electrodes. Just gently and lovingly scrap the crud off  the contacts. The same as you would take and exacto knife and scrap off a permanent marker dot on your fingernail. Be careful like that. Gently and carefully. Don't damage the socket. Clean up the lamp electrodes too if its all cruddy. 

If it looks good don't mess with it. 

Look for pinched wiring harnesses and also a wiring harness that goes from the lamps to nowhere. Maybe unplugged. Also look for dead fuses in one of the (no doubt several) fuse panels in that car. Read the electrical manual for that car. Know before you go tackle it. You are welcome to ask me for more help if you get into trouble. Look everything over carefully.