I'm gonna you how to make a alternating pulsating circuit (using 555 timer) to run a relay.
Depending on the relay you may be able to run 120vac light.
It does not alternate that good with small capacitor(I will explain later on).
Step 1: What you will need.
-1 5 pin relay (5 vdc)
-Ceramic capacitor(For reducing arcing on the relay)
-1 red LED(optionnal)
-1 green LED(optionnal)
-2 110 ohm resistor(to go with LED)
-10 to 1000 uf electrolitic capacitor
-2 1k ohm resistor
-1 555 timer