Had similar problem with my elantra, all three lights went out. Turned out to be the "brake light switch" which is right above the brake pedal. Couldn't find the part at any local auto part store so I ended up just cleaning the contacts with WD40, it works now. I am not at all suggesting you do the same thing. But it's worth playing with the switch while someone looks at the lights.
There was a large brake light switch recall that affected about 500,000 various Hyundai models including the Accent back in 2009, but IIRC it was only for '06-'07 models.
I had random complete loss of all brake lights on my '06 before the recall was ever issued. I went ahead and fixed it myself since I couldn't get it to duplicate on command for the dealer to look at. The switch was only about $10 and can be replaced in minutes with just a wrench.
Dealer,,, get your free -3K000 brake light switch... do it like ast week before you get rear ended..
Make sure they run VIN on WEBDCS for recalls, there is a PCM program out there available to update (#179), and a recent A/T program, not sure if it falls back to previous models,, check with GDS in ECU UPGRADE and update all available..