Convenience light staying on when doors are closed

I've been searching fairly extensively for topics on this but I'm not managing to find any (although I think I've found the issue with my 'wheel bearing' which sounds like it could be the dreaded sawtoothing issue), there's problems with the boot lights and the door lights but not the middle one. The problem I'm having is a bit odd, when I unlock the car the two central lights in the ceiling come on correctly but when I start the car the one for the rear passengers goes out but the main one at the front stays on. The light on the dashboard for open doors goes off which combined with the fact other lights are going off suggests the car can tell the door is closed it's just the front light that isn't reacting properly. I've tried switching it between the three different position but it doesn't seem to make any difference, in the door open position it stays on while the key is in/doors are unlocked, in the middle position it stays off completely and in the one closest to the driver it stays on. What is the proper name for this light? I've been searching under convenience light but that may not be the right term.

The car is suffering from other electrical gremlins which may or may not be related, the dash occasionally shows a flashing glow plug indicator despite the car appearing fine otherwise which a member with the identical issue and fault code traced down to a bad earth or relay. Since this was diagnosed my cruise control has gone intermittent but that may be the dirty switch and this light problem has started after both of those I believe although I don't know the exact time as it's only noticeable in darkness so I may not have spotted it due to the long days.

Thanks for any help,

John