There's a troubleshooting technique called "Half-split division." Consider a 100-bulb string. Remove the MIDDLE bulb, then check for connectivity from that socket to one end of the plug. With ONE check you've eliminated 50 bulbs.
Now in the bad half remove the bulb half-way between the plug and bulb 50, then test from that socket to the plug end and socket 50.
With TWO checks you have eliminated 75 bulbs. Repeat half-way in the bad 25-bulb string, then again in the bad 12-bulb string, then the bad 6-bulb string. Then individually check the 3 bulbs in the bad string.
