You need to be more clear...........Running lights, you talking about side markers? Those have nothing to do with the key.
Please explain what you mean "interior has power."
"Lights stay on with switch removed." You talking about the light switch? If so, you sure someone hasn't changed/ hacked the wiring? Otherwise, you have a cross in the harness "somewhere."
One example might be if the rear harness is pinched where the rear seat interacts. The dome circuit is hot all the time. If it crossed in the harness to the tail lamp circuit, it could do that. Not sure what other ways to this might be.