Electrical

It sounds like a short in the steering column or the high beam switch has shorted. You need to remove the switch and trim around the steering column to check for skinned wires, broken wires.

Not trying to but in but will share this with you What I have seen with that model car is the headlight turn signal switch go bad causing the headlight's to come on with the turn signals and with the car off and the headlight's turned off really common problem. The running light's are the high beams at half the voltage that should answer your question when the switch goes bad sometimes it only make's a part connection to the headlight's and it look's like the running light's are on. Try wiggling the high beam flash to pass switch part with the headlight's off and you may see it's the switch very clearly by the headlight's staying on.