Head and tail light electrical fault

[pothole]

Have developed some kind of fault. Here's the current situation.

Rear tail light on passenger side does not work. Have changed the bulb, no dice (original bulb actually looks fine on inspection). Rear brake light and indicator etc on passenger side work as normal.

There is also a problem with the front headlight on the same side. Dipped beam works fine, high beam works fine. But when you switch the car off with the head lights on, the passenger side turns off completely. Driver's side is fine.

I forgot to check if the passenger side headlight works in position one of the headlight switch, am guessing not.

Any ideas?