What device to find out a defective light bulb in a series circuit?

To find a faulty bulb in a series circuit, measure the voltage drop across each bulb. The bulb with the highest voltage, specifically the source voltage, is the one that is open.

In the opposite case, when the faulty bulb is shorted, it will have zero volts, while the others have slightly higher than normal voltage.

In the case of series connected Christmas Tree lights, it is a bit complicated because it is hard to measure voltage while the bulb is plugged in.

You could plug each bulb, one at a time, into a working string, or you could measure the resistance of each bulb, looking for infinity. Note, however, that modern series connected Christmas Tree lights are designed to short out when they fail, so it is a simple matter of seeing which one is not lit. (If too many bulbs, however, are shorted, the string will pull excessive current and either all bulbs will fail or the string fuse will blow.)