Dropping the fuel rods out of a reactor, away from the moderator core, coolant and the control rods? You certainly wouldn't need to worry about any lights being on if that happened!
Back to the op, I doubt that the lights would stay on for long at all, probably hours rather than days. Power stations need people to run them, yes they are automated but the automation and instrumentation is nowhere near as reliable as outsiders might think. Regular intervention is needed by the control room panel operators, without which stations would simply 'trip out' or shutdown. Even the very best set up still requires human intervention around the plant to keep it running- filters choke up and need to be changed, oil and grease must be topped up, boiler feedwater dosing tanks need to replenished, leaks spring, pumps fail, instrument air compressors fail, relief valves stick, control valves stick, instrument tappings choke up etc etc. Somebody needs to drive the shovels that load the coal!