IIRC from fiddling with my fogs, the relay actuator side loses +12V when you switch to high-beams. So you'd just have to find the low-beam relay, and give it constant +12V power on that leg (the normal headlight switch grounds the other side). I would double, triple, and quadruple check all this against the wiring diagrams obviously, I could be mis-remembering (and your car could have different wiring).
Thing is, though... I wouldn't do it anyway. You said you have projectors, so you may have separate bulbs (if you had a standard H4, this would be stupid as hell because of the heat produced), but the
wiring isn't designed for that kind of current. A 65W high-beam (typical) draws A LOT of current. Power = Current * Voltage (P=I*V), so 65W = Current * 12V. Current equals 5.4 amps. That's a fair amount of power. Plus, the voltage at the bulbs is unlikely to be 12V. It tends to be closer to 11V, because of resistance and all that, so the current will be almost 6 amps. If you toss in a 55W bulb (typical lowbeam), now you're talking about 11 amps.
PER SIDE. 22 amps is A LOT of power to be running through your dashboard. Not to mention the heat produced, nearly doubled.
I suspect the newer models that run lowbeams and highs at once have separate wiring. If you really want to do this, I would recommend you add secondary relays, very close to the bulbs (under the hood) triggered by the original relays, but hooked directly to the battery, using at least 14Ga (rated for 40A at 12V) wires (through a fuse, obviously). That will isolate the in-dash wiring from the high-current of the headlight bulbs, so if a wire burns up, it'll be the under-hood ones- less risk of fire, and easier to replace.This will also brighten the bulbs, since there's less wire for the voltage to drop across.
Whatever path you choose, do your research and be smart. Don't cut any wire unless you're damn sure what it does.
