Better yet:
The delayed interior lights have an inline diode, which might have burned to a direct conductor.
A perfect example: Older Dodge and Mopar vans, when you opened the tail gate. The front interior lamps stayed off, when the diode burned, the front interior lamps lit.
Somewhere in your circuit, you have a diode that burned, and allows pass-through and allows the lamp to stay lit.
D-C circuits go up in current when a ground is loose only when there is a wound coil; i.e. fan motor, amplifier, charged sub woofer capacitor.
Refinish King