Running lights and dash lights go out when headlights are turned on. All other lights work fine, and running lights and dash lights work when headlights are off. Have replaced all fuses...

Have you made sure that the dimmer is not turned all of the way down?

Normally this condition is the result of a poor body ground connection. Testing for this can be deceiving. At the static(nothing on) condition, testing can show a good ground. However when a circuit is excited, it has a determined resistance and a set current flow. If the ground connection to this or a branch circuit is loose, corroded, or broken wire. This will allow just enough connection to show as being good, but not good enough to complete the circuit with the required amount of connection when energized.

Theres a sensor in the middle of the dash by the front windshield that detects sunlight and triggers the automatic headlights. The main headlights and daytime running lights might be on a different circuit, in which case they daytime running lamps would turn off at night and the main headlights would turn on, indicating the main headlights arent working and the daytime running lamps are working as intended.

I would check all the fuses related to headlights, check the bulbs and check the switch, then last the light sensor on the dash.

Check the tail light bulbs, check to make sure the dash lighting switch is turned up but not turned so far up that the interior lights come on when the door is closed.

I have a 2003 GMC Sierra Z71 Extended Cab and the headlight switch won't turn off the headlights while the truck is running. When I got the truck the Photocell Sensor which is the black bubble that sits on the dash that tells the daytime running lights to turn off and on was down in the dash so I fished it out with my fingers and clipped it back in and it made the daytime running lights work. I still can't turn my headlights off while my truck is running though. The owner's manual says that I am able to do so. There's 2 light's on the switch by AUTO and the O for off that should light up? Is it my whole switch?

The running lights and dash lights are on the same circuit.The brake lights and turn signals are on their own circuit.You need to use a 12v test light to see where the circuit is broken,starting at the fuse,then the headlight switch,then the dash harness.(If the headlights work,you at least know the headlight switch is getting power).

Chk the dash light dimmer manual adjust.

This is a problewm I have been researching. On the 91 Loyale there are two headlight relays. The relay for the left headlight also controls the instrument lights and the running lights. If the right relay is working and the left is not, the left headlight will be dim because of a back electrical path through the high beam indicator light on the dash, but the instrument and running lights will be out. I have been trying to find out where Subaru put these relays, but three Subaru service departments have been no help. One dealer's service department told me to remove the large bezel around the instrument panel. I did and the relays weren't there. Lots of luck.
John

Its possible that the switch itself is the cause

Dash lights were falsing ? I assume you mean pulsing .
driving lights come on ? daytime running lights or park lamps ,does the vehicle have daytime running lamps . Daytime running lamps module .
Daytime Running Lamps (DRL) Module (Headlamp Auto Control Module)
Mounted behind the radio and the HVAC control, left of the instrument panel compartment.