Why bmw dash lights keep turning off?

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Change the license tag light bulb.
Change the left turn signal light bulb.
Change the headlight bulb.

These cars have a LKM light control module know for failure. Tons of relays and brain boxes also common failures. You need a BMW expert, and maybe someone here knows more.

electrical short in the circuit or the headlight switch itself

When you say you have power, do you mean the dash lights come on?
The power requirements of the starter motor are a lot higher than that of the dash lights or even the headlights and accessories.

Turn the headlights on and try to start the engine, if the headlights go really dim or right out then your battery doesn't have the capacity that the starter needs to turn the engine over and you need to replace it.

You don't say if it's "just" the dash lights, or if other lights do it as well. Try turning on a dome light and see if the dome light does it along with the dash lights. Do you notice your headlights doing this as well? These are just troubleshooting steps. If multiple light sources (dome, headlight, etc.) do it, then it's most likely a voltage regulator issue.

try checking your fuses first

Hi, have you checked to see if the bulb for the parking light/side light is working in the headlight?

Had a similar problem and fixed it by installing a new headlight switch / turn signal lever. Hope this helps.

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