The two wire ones look to be a bit more complicated to control. The data is sent inverted through the power wire with some cap to keep the chip powered. Some of them can only do change of color or make them all different colors. I would just return those and look for a 3-wire set of lights like WS2812B, something like this: https://www.amazon.com/BTF-LIGHTING-Decorative-Addressable-Christmas-controller/dp/B08HK67784

What we want is fully addressable fairy lights. Not the big bullet pixels that are very common.

I have these at home and they work just like any other WS2812 string. I believe the only limitation is they are not cuttable and have fixed addressing.

The one OP has we recently featured on a popular post and looked like it worked the same way. But apparently not. They don't seem to be individually addressable. But they must play some multi-plexing trickery to get different color combos rather than just solid RGB lights.