The JT-EL/FC31V3.6W-H6-IP44 is a power adapter produced by the Changzhou Jutai Electronic Company more commonly known as Czjutai.

This adapter is used with Christmas string, icicle, curtain, fairy rope lights and has 8 selectable modes via a button on the adapter.

1) Combination
2) In waves
3) Sequential
4) Slo-Glo
5) Chasing / Flash
6) Slow fade
7) Twinkle / Flash
8) Steady on.

The cable that plugs into the adapter is a 2 pin, 17mm threaded connector.

There are many similar adapters with virtually identical specifications and it is crucial that you are replacing like for like.
If the adapter you have does not match the specifications of this adapter then it will not work.