Check if the coil/injector/coil relay is stuck in the latched position. This will feed 12 to the dash/lights. You will know as the relay will be warm/hot. Cheap to replace.
Not familiar with the SC but the relays look like they are under the seat. Also consider the lights relay.
Oh FFS... Apparently there's an extra position for the key that leaves lights on for parking... I had never noticed it before. What a muppet...
@GunZenBomZ "hinted" at that in post #2 ..... All sorted now though ..... and no Ducati dealers trousered your money ! ...... Just kidding around ..... Happy Days !
As the saying goes ..... " Everyday is a school day " .... If I turn my key anti-clockwise it stops at the "Off" position , and to get parking lights I have to press it in and turn some more ...... is yours the same ? And to unlock the seat , the key only goes halfway in ..... strange !