Electronics: 2 wire LED strings on an artificial holiday tree

[Carl]

Just an electronics question.  I got an artificial holiday tree, and it is pre-lit with LEDs that do white or multi-color.  But, they only have 2 wires, so I am curious how they work.

The tree: https://www.homedepot.com/p/Home-Decorators-Collection-7-5-ft-Eastcastle-Twinkling-Balsam-Fir-LED-Pre-Lit-Artificial-Christmas-Tree-T34-25HD10003/334531283

The colors seem to be fixed per LED, so LEDs with white + one color wired in opposite polarity might be a possibility, but there is a twinkle mode where some twinkle in both white only and multicolor mode, so not sure how that would work?

I looked at the OWire library - that is a possibility, but not sure.  Those LEDs are discontinued by Sparkfun.  https://github.com/sparkfun/SparkFun_OWire_Arduino_Library

I also saw this description.  Again, not sure.  https://cpldcpu.com/2022/01/23/controlling-rgb-leds-with-only-the-powerlines-anatomy-of-a-christmas-light-string/

They do look like the ones that are linked from the above (4mm strand), but the video seems to show less capability than the ones I have.  https://www.youtube.com/watch?v=iuZZxOvY9Ls

The other question is whether the controller is in the power brick or the bottom tree segment pole.  There is also a foot pedal that cycles between modes, so maybe it is in there?

I don't want to tear it apart to attach a scope :-)

The other detail is that the first one I got only did white - no multicolor.  I exchanged it, but that led me to think there was a controller issue.  That seems to be a common issue.

If I could hack the protocol, I could add dimming etc. maybe.