Definately an earth issue o that light. Make sure the metal contact on the side of the socket is CLEAN. The metal tab on the socket is usually where a piece on the side of the socket is missing. (Often known as the locator tab).

Quote Originally Posted by playwme View Post
Tail light (or driving light as you call it) filament should go out as the brake light comes on
That's incorrect mate, it's 2 different circuits so they should both stay on if parkers are on and the brake is applied.