Interior lights are module controlled.
There is a small module on my 94 Impala SS that controls the 'auto dimming feature' of the interior lights when the car is shut off. Mine would not cut off the lights. IOW they never went out. They wouldn't come on afterwards. However I would check this module-approx. 4" by 5" green plastic box. It was in the kick panel in either the front driver's or pass. side-- it has been so long, I don't remember exactly. I THINK it was on the driver's side. If cleaning carefully with alcohol doesn't work, replace it. In the meantime, pull that fuse so you won't run down the battery.
Please note! You didn't mention what year and model B car you have and this does make a difference in the problem and solution.