Sorry to semi-necro this thread, but I just finished doing a ton of research and wanted to post the technical explanation for why this is happening. I gleaned details from my own car's wiring harness connectors, a spare SJB circuit board, and a copy of the 2016 GDS diagnostic software with technical diagrams.
In short, our cars were never meant to have the headlight DRL strip! Hyundai appears to have designed the Genesis for 3 price points. The cheapest was intended for China and had downgrades like incandescent rear turn signals and incandescent front headlights. That was never launched. The mid-price is what we got in the US, with HID headlights and the front turn signal used as a DRL. The high-price model had features like a 360 camera (Around View Monitor), self-parking (self parking assist system), brake fluid level sensor, aerodynamic flaps in the lower grille, pedestrian cushioning hood, and DRL strips in the headlights running all the time. Yes, even the 2015 model had all those features in certain markets. (Note: you can't add most of those features to your own car because the wiring harnesses and circuit boards are designed separately for each market, so some wires/connectors will be missing and you won't be able to connect the extra modules.)
Our American models obviously have a DRL strip, so what gives? I think it was added late in production, because if you look at the headlight connector, the DRL pin (#8) is not connected. Our DRL strip is run off of the side marker lights! I'm guessing Hyundai engineers always meant for our incandescent turn signal to function as a running light run during the day and night, so they also intended for it to be a 2-filament bulb so it could withstand constant use. But if the DRL strip was added at the last minute, they may have decided to save a buck and used a single filament bulb, and also keep using the old wiring harness to avoid redesigning it. So they just changed the body control firmware to run the turn signal circuit as a DRL during the daytime, and just run the side markers at night because the last-minute DRL strip is connected to them. I don't have an explanation for why the turn signal bulb isn't run at a low voltage in DRL mode, unless they thought it would respond poorly to that, or it would be difficult to have the ARISU light controller do that. (Notes: I think they called the second filament the "tell-tale lamp", which is a weird misnomer, because everywhere else that's just the formal term for "idiot lights". The side markers are called "parking lamps" and the turn signals are called "turn bulbs".)
So what can we do? Obviously, the easiest long-term fix is to replace the single filament bulb with an LED and resistor that fools the ARISU light control chips into thinking it's still an incandescent bulb, like people in this thread have done.
I wanted to do a fancier fix and control the DRL strip with my own circuit board so it runs during the day. I am rather absentminded so this is going to take a while, but I'll give some technical details here in case any other savvy people want to try. The parking lights are controlled by a ST VND5E025AK driver IC with 2 channels. The channels control the entire left and right sides of the car, from the front side marker to the rear lights to the license plate bulbs. Meanwhile, the Infineon ARISU-LT IC has no documentation, but it appears to have 3 channels. There are 2 of the ARISUs, and each connects to the left/right front turn signal, rear turn signal, and HID headlight bulb with independent channels. High beams are controlled separately by moving a small mirror with a servo. Those ICs are in the body control module/fuse box by the driver's left knee, which also contains the OBD-II diagnostnics port (which itself connects to a dedicated STM8AF52 gateway microcontroller, not one of the in-vehicle CAN networks). For some reason, Hyundai called this BCM/fuse-box a "SJB" (smart junction box) with "IPS" (intelligent power switch). The BCM/SJB is connected to all CAN networks, including the B-CAN network. To turn, the turn signal stalk sends a turn message over B-CAN and the SJB acts accordingly. If you were wondering about the indicators on the side mirrors, they are controlled by each door's control module, which is connected to B-CAN as well.
As for the next steps of my project, I don't want to bother hooking into the B-CAN network and reverse engineering the messaging format. And I bet the gateway micrcontroller that controls the lighting driver ICs has readout protection enabled. So I plan to use a custom PCB to control the front turn signals to match the rear turn signals, and power the side marker circuit when the front signals are powered but the rear signals are not. The front turn signal circuit might have a constant current supply that will provide the wrong voltage to lower resistance LEDs, so I might have to source power elsewhere. And I have to make sure this "remapping" won't make the SJB gateway controller freak out and think a bulb is burnt out. I'm a programmer by training so I'll have to enlist my irl electrical engineering friends for help designing this. Don't expect updates (I've been sitting on this for a year with little progress until today) but I hope I can eventually finish this!