Here’s a tutorial with some great background information on fixing your Christmas lights, both with incandescent and LED bulbs.
Finding the Bad Bulb
Ideally, the bad bulb will be dark while the rest of the string remains lit. But often that does not happen.
The lights in these strings are basically in series, and any open connection, whether in a wire, at a socket, or even inside a bulb, will turn off that whole circuit. Normally the bulbs have a “shunt” which shorts the bulb when it experiences full line voltage. That leaves the bad bulb OFF, and the rest of that circuit ON, which shows which bulb to replace. Unfortunately, the shunt often fails to operate, and then an entire circuit is off.
One possibility is to go down the string light-by-light and remove a bulb, test it, then put it back if it tests good. But not only is that a heck of a lot of work, it has the potential to make things much worse: When the string does not light up we cannot know that we have seated a bulb properly.
These strings generally have sockets that work well enough as long as we leave the bulbs in the socket. But when we put a bulb in, we may have to try several times before the socket makes contact. Only when the string lights up do we know we have been successful in seating a bulb. So if we are working on a dark string, we might find the bad bulb, and yet have the string still not light because several of the bulbs we re-seated are not making good contact.
Devices are sold to help with the issue of finding the bad bulb without first removing it. One sort of device picks up the 60Hz hum from a wire which is connected to the “hot” side of the AC line. Then one can follow that hum from the plug, int