The drawing below illustrates a multistage light sequencer using descrete parts and no integrated circuits. The idea is not new and I hear a similar circuit was developed about 40 years ago using germanium transistors. The idea is to connect the lights so that as one turns off it causes the next to turn on, and so forth. This is accomplished with a large capacitor between each stage that charges when a stage turns off and supplies base current to the next transistor, thus turning it on. Any number of stages can be used and the drawing below illustrates 3 small Christmas lights running at about 5 volts and 200mA. The circuit may need to be manually started when power is applied. To start it, connect a momentary short across any one of the capacitors and then remove the short. You could use a manual push button to do this.
Detailed operation:
Assume the circuit doesn't start when power is applied amd all lights are off and all three capacitors are charged to about 5 volts. We connect a jumper across the 220uF capacitor on the left which discharges the capacitor and turns on the 2nd stage transistor and corresponding light. When the jumper is removed, the capacitor will start charging through the base of the stage 2 transistor and stage 1 light. This causes the stage 2 transistor to remain on while the capacitor continues to charge. At the same time, the capacitor connecting stage 2 and 3 will discharge through the 100 ohm resistor and diode and stage 2 transistor. When the capacitor charging current falls below what is needed to keep stage 2 turned on, the transistor and light will turn off causing the voltage at the collector of the stage 2 transistor to rise to 5 volts. Since the capacitor connecting stage 2 and 3 has discharged and the voltage rises at the collector of stage 2, the capacitor from stage 2 and 3 will charge causing the 3rd stage to turn on and the cycle repeats for sucessive stages 4,5,6,7.... and back to 1. The sequence rate is determined by the capacitor and resistor values (220uF and 100 ohms in this case), load current (200mA in this case), and current gain of the particular transistor used. This arrangement runs at about 120 complete cycles per minute for 3 lights, or about 167mS per light. Faster or slower rates can be obtained with different capacitor values.