Glad you got your gap file working.
The 4-pin connectors are just standard 2.54 pitch 90deg male and female headers. Male headers come in lengths of 40 that you break into the size you want. Female headers you can get here.
I’d hold off on getting them though. That PCB was designed for curtains where you typically need 2 data pins. The 4th pin is to carry data to the second half of your curtain. But with icicles, you might need 8 data pins. So I went with just a standard 3 pin configuration. And if we can get a flex tape, the whole strip would be continuous and you’d just put a 3 pin JST-SM or waterproof connector on the end.