The passenger side headlight is very dim, replaced the light and made no difference.The running light on that side will also not work. I have check the wires for brakage and all is go as I can see. I check the fuse to the left side and that was good. Could the light work at that level if the if the relay was bad?

SOURCE: 2001 subaru outback headlight not working

chapmnfarm: your head lights use a "2" fuse system.
one for the left and one for the right.
The fuse box you are looking for is under the hood on the passenger's side. It is a black box roughly 8 inches long and 4-5 inches wide. When you remove the cover, you will see fuses and relays. What you are looking for is the section in the box which has a cluster of 7 fuses. 3 in one row and 4 in the other. On the outer parameter are two relays. The fuses you are interested in are located in the row of 4 fuses, with the two closest to the "L" shaped part of the box. Both of those should be 15 amp fuses.
The fuse below those should be a 20 amp which is the lighting switch and the one below it is a 15 amp which is for the interior lights and the clock.
Check your harness grounds in the engine compartment near the area you have the problem. There are ground wires which come out of the harness on both sides of the core support. The wires are black in color and have "EYES" crimped onto the ends of the wires. Both of them will probably be located about 4-6 inches below the upper tie bar on each side of the radiator. Odds are that the eyes will be large enough to pass a 6mm bolt through.
I hope what I have given you will resolve your problem. Lem me know,,good luck>>>>>>>>>>>>>>>

SOURCE: one headlight turns off and driving lights when brights turned on

First, it is a factory setting that turns the running lights off when the bright lights are turned on, so that's nothing to worry about. Now the headlight issue could just be a bulb. If this has a headlamp for both high and low, it is possible it just blew the high beam part. If there are seperate lamps for high and low beams, then try replacing the bulb. It should not be an electrical problem unless you had to remove or disturb alot of parts to change the wires and plugs. Let me know if this helps :)

SOURCE: Loyale Lights

Before you start 'modifying' the wiring, firstly make sure that the alternator is emitting enough charge.
There is a good chance that the carbon brushes inside, have worn out.
Hope that does it:)

SOURCE: Left low beam is inoperative. Replaced both bulbs,

I had the same problem with my 2001 Forester. Try this as a low-cost and easy repair attempt: buy brand new fuses and replace both L/H and R/H fuses. If one of your fuses is marginal, your headlights will exhibit this problem. Replacing my headlight fuses with brand new ones solved my situation.