Accessories and engine stay on while keys are out of ignition 1995 Lincoln towncar

I have a problem that just started about an hour ago. When I shut my car off, everything stays running (engine, radio). When I pulled the fuse for the instrument cluster, the car shut off. I turned it back on without the fuse connected and it started right up but the instrument cluster and radio both try to stay on (shouldn’t happen without the fuse). I plug the fuse back in while running, turn the car “off”, and I run into the same issue. What could this be? A friend of mine said it’s the BCU, but I was wanting a second opinion on what this could be.