There are two different techniques that are used to create blinking lights. One is crude and the other is sophisticated.
The crude method involves the installation of a special blinker bulb at any position in the strand. A typical blinker bulb is shown here:
The extra piece of metal at the top is a bi-metallic strip (see How Thermometers Work for details on bi-metallic strips). The current runs from the strip to the post to light the filament. When the filament gets hot, it causes the strip to bend, breaking the current and extinguishing the bulb. As the strip cools, it bends back, reconnects the post and re-lights the filament so the cycle repeats. Whenever this blinker bulb is not lit, the rest of the strand is not getting power, so the entire strand blinks in unison. Obviously, these bulbs don't have a shunt (if they did, the rest of the strand would not blink), so when the blinker bulb burns out, the rest of the strand will not light until the blinker bulb is replaced.
The more sophisticated light sets now come with 16-function controllers that can run the lights in all sorts of interesting patterns. In these systems, you typically find a controller box that is driving four separate strands of mini-bulbs. The four strands are interleaved rather than being one-after-the-other. If you ever take one of the controller boxes apart, you will find it is very simple. It contains an integrated circuit and four transistors or triacs -- one to drive each strand. The integrated circuit simply turns on a triac to light one of the four strands. By sequencing the triacs appropriately, you can create all kinds of effects! Patent 4,215,277 is a good one to read if you want to learn more about sequencers.
If you hook a mini-light bulb up to a normal AA battery, the bulb will light just like a flashlight bulb. It will be dim, however, because the bulb expects 2.5 volts rather than the 1.5 volts the battery is generating. You can put two batteries together to create 3 volts, or you can hook the bulb up to a 9-volt battery as shown here.
Because you are driving the bulb at a significantly higher voltage than it expects, it will burn extremely brightly and will not last very long (perhaps 30 minutes or an hour).
For more information on Christmas lights and all sorts of related topics, check out the links on the next page.