^^^ No, he modified it, or the previous owner did.
03-04 Tiburons have small 194-size lights to illuminate the high beam space whenever either the parking lights or full headlights are on. PLUG: I sell 194's for $2 or high-power for $8, to replace this bulb and make it pure white and brighter.
Now for whatever reason, 05-06 Tiburons have a spot for this, but it is part of the headlight molding, and is a small plastic bubble, painted like the rest of the headlight a chrome color. It can be drilled out and a light can be inserted.
Personally though, PLUG #2: I would forget the work of drilling out a city light, and instead replace it with a good set of angel eyes, such as Diode Dynamics CCFL. I'd also reccomend replacing 03-04 city lights with these.
07-08 do not have any city lights or "fake" city lights.
DRL's are standard in Korea, and as such there is a spot for the DRL relay in your fuse box from 2003 on. But for whatever reason, they were not incorporated in the U.S. versions, probably one of many changes to make the Tiburon a cheap car. DRL's are simply lights that come on at all times when the car is on. Usually, these are the headlights. Tiburons in the U.S. do not have anything like this.