How do you set up an RC circuit that will keep a 12V lamp on for 4 seconds after depressing the switch?

Use a transistor to drive a small relay. When the switch is pressed it should turn on the transistor and at the same time charge a small capacitor. Discharge the capacitor over 4 second time period with a resistor. You will have to experiment with resistors to find one that gives an acceptable discharge rate. Note, if the 12V lamp is running DC you can drive it directly with the transistor and forget about the relay.