I took a look at the DRL schematics. There appear to be two plugs going into the DRL relay, one has 4 prongs, one has 6 (of which, I believe only 4 wires are being used). The 4-prong plug, call it connector "B," needs to be plugged in since w/o it, there's no way the relay can every close. The other plug, call it "A," supplies power to one of the high beam lights when the relay is closed (high beams "on"). So if plug A is unplugged and plug B is plugged in, you can trip the DRL relay, but there will be no power going to one of the high beams. OTOH, when the relay is in the normal "off" position, you should still see both DRL high's illuminate. The reason is when the DRL's are on, the highs are in series. There's a junction in between the two lamps. When you turn the highs on, there's a power signal from the low beams to trips the relay. There are also two high beam relays, one of which powers one high beam (or both when the DRL' s are on while the other powers nothing) while the second relay only powers the other high beam when the highs are on (in this case, the relay triggers and closes the path from the second high beam relay to the second high beam light, while the junction between the two high beam lights gets a new and different path to ground, allowing both high beam lights to illuminate at full intensity.
Anyways, that said, I think the only way to disable to the DRL while keeping the high beam function is to cut the path to ground for the DRL while not altering the path to ground for the high beams. The magic lead that I think will do the trick is pin 3A of plug "A." Which one is that? If you pull the relay out and orient it so the group of 4 pins (for plug B) are on the left while the 6 pins are on the right (for plug A), pin 3A is the left-most pin on the top row of the group of 6 pins (white w/ black stripe, but careful, as there are two of them for plug A). Better yet, wire this to a manual switch in the cab so you can enable/disable the DRL's manually.
BTW, the info above on the DRL schematic is for the '03 LX. If you attempt the mod, do it at your own risk; I take no responsibility.
