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
Step 2: The Circuit
The red LED is to indicate power and the green LED is to show the speed that it is pulsing at.
I would suggest using a 330 uf electrolytic capacitor(this capacitor will determent the speed at witch the relay is pulsing the bigger the capacitor the slower the pulsing).
(Small capacitor don't alternate good, they don't give anoff time for the light to stay on.)
Step 3: Now Your Done!
I would suggest putting this in a project box.
You can pulse lights, motor and other ,anything you relay can withstand.