What is Christmas without lights? Incandescent mini-lights on the tree and GE G35 LED lights on the house.
We own an artificial tree made by GKI/Bethlehem Lighting. website 
Betty's Christmas House sells replacement components for our tree. website
Using the high-impedance oscilloscope input to detect faulty bulb on the tree.
Terry Ritter explains how mini-lights work and how to fix them. I learned something. website
EDN on building your own tester. Many comments including tips for using an oscilloscope. website
Found it. Measured with a small insulated loop around bulbs. Not sure why, just looking for repeatability on the tree. Signal on bad string was 2x normal most places and 3x in one region.
Probing for the 3x boundary I giggled one bulb and the faulty string sprang to life. We marked the trouble maker with tape so we can start there should it go out again.
We control our outdoor Christmas lights with scripts that take parameters from a web application. The scripts talk Txtzyme to a Teensy microcontroller that replaces the stock controller that came with the GE G35 LED lamps.