I have a 2001 Ford Explorer Sport Trac and the headlights are always very dim, even if the high beams are turned on.

The headlight housings are crystal clear and I bought a brand new set of basic Sylvania bulbs, but they still look awful and only give light for about 3-4 feet.

I noticed there doesn't seem to be a headlight relay so the voltage for the headlight goes through the switch. Is this a fail issue others have seen? How is the best way to go about this? I'd like to avoid going through the entire car and replacing the wiring for the headlights.

The issue affects both headlights equally.

 

You have , as I see it, 3 choices.

You can go through the entire wiring connections hoping to find the problem.
You can invest in a small multimeter ,do voltage drop testing to verify proper power is available to the front lights , including ground connections.
You can have a good shop check it out.

As a last resort, just remove , clean and reinstall all the ground wire connections at the front of the vehicle. One of them provides the ground path for the headlights.
Let us know if you require further assistance.