If they are 1/2 way smart a $6.00 meter from harbor Freight could work. They don't have auto-off function, so power from a suitable 9V supply (I think). I can look at mine.
The diode test will do 90% of probaby what you need.
Fuses and LED's.
So, what you might do is:
1) make a 9V power supply
2) Make something that will hold the bulbs.
3) Add an easy reverse polarity switch.
4) That get's you fuse and basic LED testing.
5) For a little more testing, add a current source using an LM334 or an LT part and set the current to 50 mA.
Their little polarity tester, should make sure the voltage reads above 2.1 V.
Push another button and the bulb should light.
So:
1. we have a basic ceap meter always set to diode test.
2. We add an isolated 9V power supply because no auto off.
3. We add fuseholders and LED sockets in parallel.
4. A DPDT switch to set polarity.
e.g Insert bulb, flip DPDT swith
Reads 0 in both directions - bad
Reads 0 and >1.2, probably good.
Leave the DPDT switch in the >1.2 position
Push another switch and it would add an LED and the current source in series.
Light should light. If a blinker bulb is inserted, it should blink.
The first thought that came to me, was plug the set in.
I never quite developed a technique for finding a bad bulb in a string, One is easy. 2 or more is miserable.
I tried a contactless voltage probe. You must use a polarized connector. Never tried a TDR. That might work.
Measuring voltages and bisecting always sounds like a good idea,
Remember that some of the incadescent bulbs have a ring that shorts the filiment. Watch out for the blinker bulbs too.
Testing of 120 V strings should be done with an isolation xformer or voltages below 24 VAC. I've never tried that either.