For anyone reviewing this thread: No load resistors are needed. I simply used an inline 330 ohm resistor to dim the running lights, 2 diodes to prevent back feeding, and a new ground. Resulting power dissipated by the inline resistor is on the order of 0.10 watt.
Interesting; I had considered something like this myself, but I wanted to see where I could get with the "standard" way.
Does it play well with having all the other lamps (front and rear) being LEDs as well? Also, does the relay care? I might play around with this in the future.
Right now, with my current setup, when I just have my running lights on - if I use my turn signal the front signal works fine, and when not signalling it stays lit, like it should. The side marker lamp (also LED), though, is weird - when not signaling, it's lit up properly - but when signaling, it "flashes" with a quick pulse - I am not sure why. It's not much of a factor for me, because I rarely use only my running lights - usually I have my headlights on if I need the running lights. Strangely, with my headlights on - both turn signals work properly!
In the future, I have an idea that I'm hoping will work out, if I can figure out a simple way to do it. Right now, the "complex way" involves a small microcontroller at worst - but I think if I cipher on it long enough, I can reduce the logic to a relay or two, and maybe some diodes...
But anyhow, what I want to do is add a DRL element to the running lights. I bought a set of clear front markers, and then a set of LED bulbs that are "alternating" amber/white depending on the direction of current thru them. If you have them set up properly, then with regular running lights, they should be amber, but when flashing, they alternate amber/white.
What I want to do is make them run white all the time, but when flashing, turn off the white and flash only the amber. It could probably be handled with a circuit like you mentioned, plus an extra SPDT relay that only turns on with the running lights activated. I'm sure the logic is simple, I just haven't taken the time to really think about it fully. Plus there'd need to be something to keep the side marker lit with the running light, but also allow it to flash as well.
If I can figure it out, it'd give me a nice option for DRLs without needing to purchase expensive LED headlights with the rings (I'm actually going to try a set of JK headlights with some LED bulbs in them to see how that works out - anything has to be better than the standard sealed lamps I currently have).