I am confident that there is a dedicated ground near the front of the car. follow the wire from the back of the headlight housing 'upstream'. There should be a wire somewhere along there that goes to a screw in the body. In fact, I am pretty sure that there is one such screw at the extreme outer edges of the upper radiator support (the piece of sheet metal just in front of the radiator). I remember removing it and adding the ground for my ignition to the passengers side screw.
If you see a screw or bolt in the body that has a wire under it, it is a ground. The battery is connected to the body (usually via the engine block) and so you can ground any electrical device anywhere on the car to the body.... for instance the tail lamps are grounded near the rear of the car. The whole body acts as a ground.
You can probably check if it's a ground problem by unhooking the headlight, run a jumper wire from the body harness to the corresponding pin on the lamp. Then wire another jumper from another pin on the light to the body. Turn the lights on. If the light is 'normal' illumination, then the problem is most likely ground related. If there are more than two pins in the connector (most likely with the headlights) one is high beam and will only be on when the high beams are.... try them all, you can't hurt it as long as the light itself is between the two jumpers you installed.
Checking a ground it pretty easy if you have a voltmeter too. If you do, set it to 'Ohms' and (with the lights off) put one lead on any of the pins in the connector on the wire harness and the other on bare sheetmetal. If the meter does not chage at all, try a different pin in the connector. One of the pins will be ground. When you find ground, the meter will read 'something' close to zero. If the number is much more then zero, I would say you have a problem with the ground strap in that harness... you need to trace it upstream like I mentioned before.
Good luck.